Daily Papers

Deep research models perform multi-step research to produce long-form, well-attributed answers. However, most open deep research models are trained on easily verifiable short-form QA tasks via reinforcement learning with verifiable rewards (RLVR), which does not extend to realistic long-form tasks. We address this with Reinforcement Learning with Evolving Rubrics (RLER), in which we construct and maintain rubrics that co-evolve with the policy model during training; this allows the rubrics to incorporate information that the model has newly explored and to provide discriminative, on-policy feedback. Using RLER, we develop Deep Research Tulu (DR Tulu-8B), the first open model that is directly trained for open-ended, long-form deep research. Across four long-form deep research benchmarks in science, healthcare and general domains, DR Tulu substantially outperforms existing open deep research models, and matches or exceeds proprietary deep research systems, while being significantly smaller and cheaper per query. To facilitate future research, we release all data, models, and code, including our new MCP-based agent infrastructure for deep research systems.

Standard reward models typically predict scalar scores that fail to capture the multifaceted nature of response quality in non-verifiable domains, such as creative writing or open-ended instruction following. To address this limitation, we propose Rubric-ARM, a framework that jointly optimizes a rubric generator and a judge using reinforcement learning from preference feedback. Unlike existing methods that rely on static rubrics or disjoint training pipelines, our approach treats rubric generation as a latent action learned to maximize judgment accuracy. We introduce an alternating optimization strategy to mitigate the non-stationarity of simultaneous updates, providing theoretical analysis that demonstrates how this schedule reduces gradient variance during training. Extensive experiments show that Rubric-ARM achieves state-of-the-art performance among baselines on multiple benchmarks and significantly improves downstream policy alignment in both offline and online reinforcement learning settings.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a prevailing paradigm for enhancing reasoning in Multimodal Large Language Models (MLLMs). However, relying solely on outcome supervision risks reward hacking, where models learn spurious reasoning patterns to satisfy final answer checks. While recent rubric-based approaches offer fine-grained supervision signals, they suffer from high computational costs of instance-level generation and inefficient training dynamics caused by treating all rubrics as equally learnable. In this paper, we propose Stratified Rubric-based Curriculum Learning (RuCL), a novel framework that reformulates curriculum learning by shifting the focus from data selection to reward design. RuCL generates generalized rubrics for broad applicability and stratifies them based on the model's competence. By dynamically adjusting rubric weights during training, RuCL guides the model from mastering foundational perception to tackling advanced logical reasoning. Extensive experiments on various visual reasoning benchmarks show that RuCL yields a remarkable +7.83% average improvement over the Qwen2.5-VL-7B model, achieving a state-of-the-art accuracy of 60.06%.

Rubric-based Reinforcement Learning (RL) has emerged as a promising approach for aligning Large Language Models (LLMs) with complex, open-domain instruction following tasks. However, existing methods predominantly rely on response-level rewards, introducing severe reward sparsity and reward ambiguity problems. To address these issues, we propose Rubrics to Tokens (RTT), a novel rubric-based RL framework that bridges coarse response-level scores and fine-grained token-level credit assignment. RTT introduces a Token-Level Relevance Discriminator to predict which tokens in the response are responsible for a specific constraint, and optimizes the policy model via RTT-GRPO, which integrates response-level and token-level advantages within a unified framework. Furthermore, when transitioning from one-dimensional, outcome-level reward to three-dimensional reward space in the token-level rubric-based RL, we propose a novel group normalization method, called Intra-sample Token Group Normalization, to accommodate this shift. Extensive experiments and benchmarks demonstrate that RTT consistently outperforms other baselines in both instruction- and rubric-level accuracy across different models.

Rubrics provide a flexible way to train LLMs on open-ended long-form answers where verifiable rewards are not applicable and human preferences provide coarse signals. Prior work shows that reinforcement learning with rubric-based rewards leads to consistent gains in LLM post-training. Most existing approaches rely on rubrics that remain static over the course of training. Such static rubrics, however, are vulnerable to reward-hacking type behaviors and fail to capture emergent desiderata that arise during training. We introduce Online Rubrics Elicitation (OnlineRubrics), a method that dynamically curates evaluation criteria in an online manner through pairwise comparisons of responses from current and reference policies. This online process enables continuous identification and mitigation of errors as training proceeds. Empirically, this approach yields consistent improvements of up to 8% over training exclusively with static rubrics across AlpacaEval, GPQA, ArenaHard as well as the validation sets of expert questions and rubrics. We qualitatively analyze the elicited criteria and identify prominent themes such as transparency, practicality, organization, and reasoning.

Reward modeling lies at the core of reinforcement learning from human feedback (RLHF), yet most existing reward models rely on scalar or pairwise judgments that fail to capture the multifaceted nature of human preferences. Recent studies have explored rubrics-as-rewards (RaR) that uses structured natural language criteria that capture multiple dimensions of response quality. However, producing rubrics that are both reliable and scalable remains a key challenge. In this work, we introduce OpenRubrics, a diverse, large-scale collection of (prompt, rubric) pairs for training rubric-generation and rubric-based reward models. To elicit discriminative and comprehensive evaluation signals, we introduce Contrastive Rubric Generation (CRG), which derives both hard rules (explicit constraints) and principles (implicit qualities) by contrasting preferred and rejected responses. We further improve reliability by enforcing preference-label consistency via rejection sampling to remove noisy rubrics. Across multiple reward-modeling benchmarks, our rubric-based reward model, Rubric-RM, surpasses strong size-matched baselines by 6.8%. These gains transfer to policy models on instruction-following and biomedical benchmarks. Our results show that rubrics provide scalable alignment signals that narrow the gap between costly human evaluation and automated reward modeling, enabling a new principle-driven paradigm for LLM alignment.

Reinforcement Learning with Verifiable Rewards (RLVR) has driven substantial progress in reasoning-intensive domains like mathematics. However, optimizing open-ended generation remains challenging due to the lack of ground truth. While rubric-based evaluation offers a structured proxy for verification, existing methods suffer from scalability bottlenecks and coarse criteria, resulting in a supervision ceiling effect. To address this, we propose an automated Coarse-to-Fine Rubric Generation framework. By synergizing principle-guided synthesis, multi-model aggregation, and difficulty evolution, our approach produces comprehensive and highly discriminative criteria capable of capturing the subtle nuances. Based on this framework, we introduce RubricHub, a large-scale (sim110k) and multi-domain dataset. We validate its utility through a two-stage post-training pipeline comprising Rubric-based Rejection Sampling Fine-Tuning (RuFT) and Reinforcement Learning (RuRL). Experimental results demonstrate that RubricHub unlocks significant performance gains: our post-trained Qwen3-14B achieves state-of-the-art (SOTA) results on HealthBench (69.3), surpassing proprietary frontier models such as GPT-5. The code and data will be released soon.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing Large Language Models (LLMs), exemplified by the success of OpenAI's o-series. In RLVR, rewards are derived from verifiable signals-such as passing unit tests in code generation or matching correct answers in mathematical reasoning. While effective, this requirement largely confines RLVR to domains with automatically checkable outcomes. To overcome this, we extend the RLVR paradigm to open-ended tasks by integrating rubric-based rewards, where carefully designed rubrics serve as structured, model-interpretable criteria for automatic scoring of subjective outputs. We construct, to our knowledge, the largest rubric reward system to date, with over 10,000 rubrics from humans, LLMs, or a hybrid human-LLM collaboration. Implementing rubric-based RL is challenging; we tackle these issues with a clear framework and present an open-sourced Qwen-30B-A3B model with notable gains: 1) With only 5K+ samples, our system improves by +5.2% on open-ended benchmarks (especially humanities), outperforming a 671B DeepSeek-V3 model by +2.4%, while preserving general and reasoning abilities. 2) Our method provides fine-grained stylistic control, using rubrics as anchors to mitigate the "AI-like" tone and produce more human-like, expressive responses. We share key lessons in rubric construction, data selection, and training, and discuss limitations and future releases.

Recent advances in reinforcement learning (RL) have significantly improved the complex reasoning capabilities of large language models (LLMs). Despite these successes, existing methods mainly focus on single-domain RL (e.g., mathematics) with verifiable rewards (RLVR), and their reliance on purely online RL frameworks restricts the exploration space, thereby limiting reasoning performance. In this paper, we address these limitations by leveraging rubrics to provide both fine-grained reward signals and offline guidance. We propose RGR-GRPO (Reward and Guidance through Rubrics), a rubric-driven RL framework for multi-domain reasoning. RGR-GRPO enables LLMs to receive dense and informative rewards while exploring a larger solution space during GRPO training. Extensive experiments across 14 benchmarks spanning multiple domains demonstrate that RGR-GRPO consistently outperforms RL methods that rely solely on alternative reward schemes or offline guidance. Compared with verifiable online RL baseline, RGR-GRPO achieves average improvements of +7.0%, +5.4%, +8.4%, and +6.6% on mathematics, physics, chemistry, and general reasoning tasks, respectively. Notably, RGR-GRPO maintains stable entropy fluctuations during off-policy training and achieves superior pass@k performance, reflecting sustained exploration and effective breakthrough beyond existing performance bottlenecks.

Reinforcement Learning (RL) with rubric-based rewards has recently shown remarkable progress in enhancing general reasoning capabilities of Large Language Models (LLMs), yet still suffers from ineffective exploration confined to curent policy distribution. In fact, RL optimization can be viewed as steering the policy toward an ideal distribution that maximizes the rewards, while effective exploration should align efforts with desired target. Leveraging this insight, we propose HeRL, a Hindsight experience guided Reinforcement Learning framework to bootstrap effective exploration by explicitly telling LLMs the desired behaviors specified in rewards. Concretely, HeRL treats failed trajectories along with their unmet rubrics as hindsight experience, which serves as in-context guidance for the policy to explore desired responses beyond its current distribution. Additionally, we introduce a bonus reward to incentivize responses with greater potential for improvement under such guidance. HeRL facilitates effective learning from desired high quality samples without repeated trial-and-error from scratch, yielding a more accurate estimation of the expected gradient theoretically. Extensive experiments across various benchmarks demonstrate that HeRL achieves superior performance gains over baselines, and can further benefit from experience guided self-improvement at test time. Our code is available at https://github.com/sikelifei/HeRL.

Recent advances in Large Language Models (LLMs) have underscored the potential of Reinforcement Learning (RL) to facilitate the emergence of reasoning capabilities. Despite the encouraging results, a fundamental dilemma persists as RL improvement relies on learning from high-quality samples, yet the exploration for such samples remains bounded by the inherent limitations of LLMs. This, in effect, creates an undesirable cycle in which what cannot be explored cannot be learned. In this work, we propose Rubric-Scaffolded Reinforcement Learning (RuscaRL), a novel instructional scaffolding framework designed to break the exploration bottleneck for general LLM reasoning. Specifically, RuscaRL introduces checklist-style rubrics as (1) explicit scaffolding for exploration during rollout generation, where different rubrics are provided as external guidance within task instructions to steer diverse high-quality responses. This guidance is gradually decayed over time, encouraging the model to internalize the underlying reasoning patterns; (2) verifiable rewards for exploitation during model training, where we can obtain robust LLM-as-a-Judge scores using rubrics as references, enabling effective RL on general reasoning tasks. Extensive experiments demonstrate the superiority of the proposed RuscaRL across various benchmarks, effectively expanding reasoning boundaries under the best-of-N evaluation. Notably, RuscaRL significantly boosts Qwen-2.5-7B-Instruct from 23.6 to 50.3 on HealthBench-500, surpassing GPT-4.1. Furthermore, our fine-tuned variant on Qwen3-30B-A3B-Instruct achieves 61.1 on HealthBench-500, outperforming leading LLMs including OpenAI-o3.

Extending Reinforcement Learning with Verifiable Rewards (RLVR) to real-world tasks often requires balancing objective and subjective evaluation criteria. However, many such tasks lack a single, unambiguous ground truth-making it difficult to define reliable reward signals for post-training language models. While traditional preference-based methods offer a workaround, they rely on opaque reward functions that are difficult to interpret and prone to spurious correlations. We introduce Rubrics as Rewards (RaR), a framework that uses structured, checklist-style rubrics as interpretable reward signals for on-policy training with GRPO. Our best RaR method yields up to a 28% relative improvement on HealthBench-1k compared to simple Likert-based approaches, while matching or surpassing the performance of reward signals derived from expert-written references. By treating rubrics as structured reward signals, we show that RaR enables smaller-scale judge models to better align with human preferences and sustain robust performance across model scales.

Open-ended generation tasks require outputs to satisfy diverse and often implicit task-specific evaluation rubrics. The sheer number of relevant rubrics leads to prohibitively high verification costs and incomplete assessments of a response, making reinforcement learning (RL) post-training with rubric-based rewards difficult to scale. This problem is exacerbated by the fact that often the best way to combine these rubrics into one single reward is also highly prompt-specific. We propose Reinforcement Learning with Adversarial Critic (RLAC), a post-training approach that addresses these challenges via dynamic rubric verification. Our approach employs a large language model (LLM) as a critic that dynamically identifies only the most likely failure modes (e.g., a factual error or unhandled edge case), which are then verified by an external validator to optimize both generator and critic jointly. By training both the generator and the critic, this game enhances the critic's error detection and the generator's output quality while reducing required verifications. Our experiments demonstrate that RLAC improves factual accuracy in text generation and correctness in code generation, while also outperforming exhaustive verification and reward model methods. We show that dynamic critics are more effective than fixed critics, showcasing the potential of RLAC for scaling RL post-training to free-form generation tasks.

Scalar reward models compress multi-dimensional human preferences into a single opaque score, creating an information bottleneck that often leads to brittleness and reward hacking in open-ended alignment. We argue that robust alignment for non-verifiable tasks is fundamentally a principle generalization problem: reward should not be a learned function internalized into a judge, but an explicit reasoning process executed under inspectable principles. To operationalize this view, we present the Open Rubric System (OpenRS), a plug-and-play, rubrics-based LLM-as-a-Judge framework built around Pairwise Adaptive Meta-Rubrics (PAMR) and lightweight Pointwise Verifiable Rubrics (PVRs), which provide both hard-constraint guardrails and verifiable reward components when ground-truth or programmatic checks are available. OpenRS uses an explicit meta-rubric -- a constitution-like specification that governs how rubrics are instantiated, weighted, and enforced -- and instantiates adaptive rubrics on the fly by conditioning on the semantic differences between two candidate responses. It then performs criterion-wise pairwise comparisons and aggregates criterion-level preferences externally, avoiding pointwise weighted scalarization while improving discriminability in open-ended settings. To keep principles consistent yet editable across various domains, we introduce a two-level meta-rubric refinement pipeline (automated evolutionary refinement for general principles and a reproducible human-in-the-loop procedure for domain principles), complemented with pointwise verifiable rubrics that act as both guardrails against degenerate behaviors and a source of verifiable reward for objective sub-tasks. Finally, we instantiate OpenRS as reward supervision in pairwise RL training.

Recently, rubrics have been used to guide LLM judges in capturing subjective, nuanced, multi-dimensional human preferences, and have been extended from evaluation to reward signals for reinforcement fine-tuning (RFT). However, rubric generation remains hard to control: rubrics often lack coverage, conflate dimensions, misalign preference direction, and contain redundant or highly correlated criteria, degrading judge accuracy and producing suboptimal rewards during RFT. We propose RRD, a principled framework for rubric refinement built on a recursive decompose-filter cycle. RRD decomposes coarse rubrics into fine-grained, discriminative criteria, expanding coverage while sharpening separation between responses. A complementary filtering mechanism removes misaligned and redundant rubrics, and a correlation-aware weighting scheme prevents over-representing highly correlated criteria, yielding rubric sets that are informative, comprehensive, and non-redundant. Empirically, RRD delivers large, consistent gains across both evaluation and training: it improves preference-judgment accuracy on JudgeBench and PPE for both GPT-4o and Llama3.1-405B judges, achieving top performance in all settings with up to +17.7 points on JudgeBench. When used as the reward source for RFT on WildChat, it yields substantially stronger and more stable learning signals, boosting reward by up to 160% (Qwen3-4B) and 60% (Llama3.1-8B) versus 10-20% for prior rubric baselines, with gains that transfer to HealthBench-Hard and BiGGen Bench. Overall, RRD establishes recursive rubric refinement as a scalable and interpretable foundation for LLM judging and reward modeling in open-ended domains.

Nowadays, training and evaluating DeepResearch-generated reports remain challenging due to the lack of verifiable reward signals. Accordingly, rubric-based evaluation has become a common practice. However, existing approaches either rely on coarse, pre-defined rubrics that lack sufficient granularity, or depend on manually constructed query-specific rubrics that are costly and difficult to scale. In this paper, we propose a pipeline to train human-preference-aligned query-specific rubric generators tailored for DeepResearch report generation. We first construct a dataset of DeepResearch-style queries annotated with human preferences over paired reports, and train rubric generators via reinforcement learning with a hybrid reward combining human preference supervision and LLM-based rubric evaluation. To better handle long-horizon reasoning, we further introduce a Multi-agent Markov-state (MaMs) workflow for report generation. We empirically show that our proposed rubric generators deliver more discriminative and better human-aligned supervision than existing rubric design strategies. Moreover, when integrated into the MaMs training framework, DeepResearch systems equipped with our rubric generators consistently outperform all open-source baselines on the DeepResearch Bench and achieve performance comparable to that of leading closed-source models.

Large Language Models (LLMs) have shown substantial advances through reinforcement learning (RL), particularly in domains where rewards can be programmatically verified, such as mathematics and code. In these areas, models benefit from a well-defined operational base guided by explicit rule-based objectives. However, this progress reveals a significant limitation: in open-ended domains where rewards are ambiguous, subjective, or context-dependent, such as creative writing, scientific reasoning, and notably medical consultation, robust reward functions are lacking, making these areas challenging for current RL strategies. To bridge this gap, we introduce ORBIT, an open-ended rubric-based incremental training framework specifically designed for high-stakes medical dialogue. ORBIT integrates syn- thetic dialogue generation with the dynamic creation of rubrics, employing these rubrics to direct an incremental RL process. In particular, this approach does not depend on external medical knowledge or manual rules, instead utilizing rubric-guided feedback to shape learning. When implemented on the Qwen3-4B-Instruct model, our method can greatly enhance its performance on the HealthBench-Hard benchmark from 7.0 to 27.2 using only 2k samples, thus achieving state-of-the-art results for models of this scale. Our analysis confirms that rubric-driven RL fos-ters consistent performance gains across diverse consultation scenarios, going beyond simple numerical improvements. These findings underscore rubric-based feedback as a scalable strategy for advancing LLMs in intricate, open-ended tasks.

Open-ended evaluation is essential for deploying large language models in real-world settings. In studying HealthBench, we observe that using the model itself as a grader and generating rubric-based reward signals substantially improves reasoning performance. Remarkably, the trained model also becomes a stronger grader. Motivated by this, we introduce Self-Rewarding Rubric-Based Reinforcement Learning for Open-Ended Reasoning, a lightweight framework that enables faster and more resource-efficient training while surpassing baselines. Remarkably, on Qwen3-32B, training with just the 4000-sample HealthBench Easy subset is sufficient to obtain a model that exceeds GPT-5 on HealthBench Hard. Incorporating a small amount of teacher-graded data further enhances performance for less capable models.

Recent progress in large language models (LLMs) has led to impressive performance on a range of tasks, yet advanced instruction following (IF)-especially for complex, multi-turn, and system-prompted instructions-remains a significant challenge. Rigorous evaluation and effective training for such capabilities are hindered by the lack of high-quality, human-annotated benchmarks and reliable, interpretable reward signals. In this work, we introduce AdvancedIF (we will release this benchmark soon), a comprehensive benchmark featuring over 1,600 prompts and expert-curated rubrics that assess LLMs ability to follow complex, multi-turn, and system-level instructions. We further propose RIFL (Rubric-based Instruction-Following Learning), a novel post-training pipeline that leverages rubric generation, a finetuned rubric verifier, and reward shaping to enable effective reinforcement learning for instruction following. Extensive experiments demonstrate that RIFL substantially improves the instruction-following abilities of LLMs, achieving a 6.7% absolute gain on AdvancedIF and strong results on public benchmarks. Our ablation studies confirm the effectiveness of each component in RIFL. This work establishes rubrics as a powerful tool for both training and evaluating advanced IF in LLMs, paving the way for more capable and reliable AI systems.

Despite chain-of-thought (CoT) playing crucial roles in LLM reasoning, directly rewarding it is difficult: training a reward model demands heavy human labeling efforts, and static RMs struggle with evolving CoT distributions and reward hacking. These challenges motivate us to seek an autonomous CoT rewarding approach that requires no human annotation efforts and can evolve gradually. Inspired by recent self-evolving training methods, we propose RLCER (Reinforcement Learning with CoT Supervision via Self-Evolving Rubrics), which enhances the outcome-centric RLVR by rewarding CoTs with self-proposed and self-evolving rubrics. We show that self-proposed and self-evolving rubrics provide reliable CoT supervision signals even without outcome rewards, enabling RLCER to outperform outcome-centric RLVR. Moreover, when used as in-prompt hints, these self-proposed rubrics further improve inference-time performance.

Evolutionary Reinforcement Learning (ERL), which integrates Evolutionary Algorithms (EAs) and Reinforcement Learning (RL) for optimization, has demonstrated remarkable performance advancements. By fusing both approaches, ERL has emerged as a promising research direction. This survey offers a comprehensive overview of the diverse research branches in ERL. Specifically, we systematically summarize recent advancements in related algorithms and identify three primary research directions: EA-assisted Optimization of RL, RL-assisted Optimization of EA, and synergistic optimization of EA and RL. Following that, we conduct an in-depth analysis of each research direction, organizing multiple research branches. We elucidate the problems that each branch aims to tackle and how the integration of EAs and RL addresses these challenges. In conclusion, we discuss potential challenges and prospective future research directions across various research directions. To facilitate researchers in delving into ERL, we organize the algorithms and codes involved on https://github.com/yeshenpy/Awesome-Evolutionary-Reinforcement-Learning.

Recently, reward-conditioned reinforcement learning (RCRL) has gained popularity due to its simplicity, flexibility, and off-policy nature. However, we will show that current RCRL approaches are fundamentally limited and fail to address two critical challenges of RCRL -- improving generalization on high reward-to-go (RTG) inputs, and avoiding out-of-distribution (OOD) RTG queries during testing time. To address these challenges when training vanilla RCRL architectures, we propose Bayesian Reparameterized RCRL (BR-RCRL), a novel set of inductive biases for RCRL inspired by Bayes' theorem. BR-RCRL removes a core obstacle preventing vanilla RCRL from generalizing on high RTG inputs -- a tendency that the model treats different RTG inputs as independent values, which we term ``RTG Independence". BR-RCRL also allows us to design an accompanying adaptive inference method, which maximizes total returns while avoiding OOD queries that yield unpredictable behaviors in vanilla RCRL methods. We show that BR-RCRL achieves state-of-the-art performance on the Gym-Mujoco and Atari offline RL benchmarks, improving upon vanilla RCRL by up to 11%.

Small LLMs often struggle to match the agentic capabilities of large, costly models. While reinforcement learning can help, progress has been limited by two structural bottlenecks: existing open-source agentic training data are narrow in task variety and easily solved; real-world APIs lack diversity and are unstable for large-scale reinforcement learning rollout processes. We address these challenges with SYNTHAGENT, a framework that jointly synthesizes diverse tool-use training data and simulates complete environments. Specifically, a strong teacher model creates novel tasks and tool ecosystems, then rewrites them into intentionally underspecified instructions. This compels agents to actively query users for missing details. When handling synthetic tasks, an LLM-based user simulator provides user-private information, while a mock tool system delivers stable tool responses. For rewards, task-level rubrics are constructed based on required subgoals, user-agent interactions, and forbidden behaviors. Across 14 challenging datasets in math, search, and tool use, models trained on our synthetic data achieve substantial gains, with small models outperforming larger baselines.

Reinforcement learning (RL) has emerged as a critical technique for enhancing LLM-based deep search agents. However, existing approaches primarily rely on binary outcome rewards, which fail to capture the comprehensiveness and factuality of agents' reasoning process, and often lead to undesirable behaviors such as shortcut exploitation and hallucinations. To address these limitations, we propose Citation-aware Rubric Rewards (CaRR), a fine-grained reward framework for deep search agents that emphasizes reasoning comprehensiveness, factual grounding, and evidence connectivity. CaRR decomposes complex questions into verifiable single-hop rubrics and requires agents to satisfy these rubrics by explicitly identifying hidden entities, supporting them with correct citations, and constructing complete evidence chains that link to the predicted answer. We further introduce Citation-aware Group Relative Policy Optimization (C-GRPO), which combines CaRR and outcome rewards for training robust deep search agents. Experiments show that C-GRPO consistently outperforms standard outcome-based RL baselines across multiple deep search benchmarks. Our analysis also validates that C-GRPO effectively discourages shortcut exploitation, promotes comprehensive, evidence-grounded reasoning, and exhibits strong generalization to open-ended deep research tasks. Our code and data are available at https://github.com/THUDM/CaRR.

Reinforcement Learning (RL) has demonstrated significant potential in enhancing the reasoning capabilities of large language models (LLMs). However, the success of RL for LLMs heavily relies on human-curated datasets and verifiable rewards, which limit their scalability and generality. Recent Self-Play RL methods, inspired by the success of the paradigm in games and Go, aim to enhance LLM reasoning capabilities without human-annotated data. However, their methods primarily depend on a grounded environment for feedback (e.g., a Python interpreter or a game engine); extending them to general domains remains challenging. To address these challenges, we propose Multi-Agent Evolve (MAE), a framework that enables LLMs to self-evolve in solving diverse tasks, including mathematics, reasoning, and general knowledge Q&A. The core design of MAE is based on a triplet of interacting agents (Proposer, Solver, Judge) that are instantiated from a single LLM, and applies reinforcement learning to optimize their behaviors. The Proposer generates questions, the Solver attempts solutions, and the Judge evaluates both while co-evolving. Experiments on Qwen2.5-3B-Instruct demonstrate that MAE achieves an average improvement of 4.54% on multiple benchmarks. These results highlight MAE as a scalable, data-efficient method for enhancing the general reasoning abilities of LLMs with minimal reliance on human-curated supervision.

Current reinforcement learning (RL) frameworks for large language models (LLM) post-training typically assume a fixed prompt distribution, which is sub-optimal and bottlenecks scalability. Prior works have explored prompt evolving, but are often limited to the supervised fine-tuning stage, and prompts are sampled and evolved uniformly without signals. This empirical work presents a paradigm shift: Evolving Alignment via Asymmetric Self-Play (eva), that casts post-training as an infinite game with regret-based signals for 2 players: (i) a creator, who strategically samples and creates new informative prompts and (ii) a solver, who learns to produce preferred responses. eva is the first method that allows language models to adaptively create training prompts in both offline and online RL post-training. The design is simple, easy-to-use yet remarkably effective: eva sets a new SOTA on challenging benchmarks, without any extra human prompts, e.g. it boosts the win-rate of gemma-2-9b-it on Arena-Hard by 51.6% -> 60.1% for DPO and 52.6% -> 62.4% for RLOO, surpassing claude-3-opus and catching up to gemini-1.5-pro, both of which are orders of magnitude larger. Extensive experiments show eva can create effective RL curricula and is robust across ablations. We believe adaptively evolving prompts are key to designing the next-generation RL post-training scheme.

Reinforcement learning is the method of choice to train models in sampling-based setups with binary outcome feedback, such as navigation, code generation, and mathematical problem solving. In such settings, models implicitly induce a likelihood over correct rollouts. However, we observe that reinforcement learning does not maximize this likelihood, and instead optimizes only a lower-order approximation. Inspired by this observation, we introduce Maximum Likelihood Reinforcement Learning (MaxRL), a sampling-based framework to approximate maximum likelihood using reinforcement learning techniques. MaxRL addresses the challenges of non-differentiable sampling by defining a compute-indexed family of sample-based objectives that interpolate between standard reinforcement learning and exact maximum likelihood as additional sampling compute is allocated. The resulting objectives admit a simple, unbiased policy-gradient estimator and converge to maximum likelihood optimization in the infinite-compute limit. Empirically, we show that MaxRL Pareto-dominates existing methods in all models and tasks we tested, achieving up to 20x test-time scaling efficiency gains compared to its GRPO-trained counterpart. We also observe MaxRL to scale better with additional data and compute. Our results suggest MaxRL is a promising framework for scaling RL training in correctness based settings.

While reinforcement learning (RL) shows remarkable success in decision-making problems, it often requires a lot of interactions with the environment, and in sparse-reward environments, it is challenging to learn meaningful policies. Large Language Models (LLMs) can potentially provide valuable guidance to agents in learning policies, thereby enhancing the performance of RL algorithms in such environments. However, LLMs often encounter difficulties in understanding downstream tasks, which hinders their ability to optimally assist agents in these tasks. A common approach to mitigating this issue is to fine-tune the LLMs with task-related data, enabling them to offer useful guidance for RL agents. However, this approach encounters several difficulties, such as inaccessible model weights or the need for significant computational resources, making it impractical. In this work, we introduce RLAdapter, a framework that builds a better connection between RL algorithms and LLMs by incorporating an adapter model. Within the RLAdapter framework, fine-tuning a lightweight language model with information generated during the training process of RL agents significantly aids LLMs in adapting to downstream tasks, thereby providing better guidance for RL agents. We conducted experiments to evaluate RLAdapter in the Crafter environment, and the results show that RLAdapter surpasses the SOTA baselines. Furthermore, agents under our framework exhibit common-sense behaviors that are absent in baseline models.

Reinforcement Learning with Verifiable Rewards (RLVR) has demonstrated promising gains in enhancing the reasoning capabilities of large language models. However, its dependence on domain-specific verifiers significantly restricts its applicability to open and general domains. Recent efforts such as RLPR have extended RLVR to general domains, enabling training on broader datasets and achieving improvements over RLVR. However, a notable limitation of these methods is their tendency to overfit to reference answers, which constrains the model's ability to generate diverse outputs. This limitation is particularly pronounced in open-ended tasks such as writing, where multiple plausible answers exist. To address this, we propose DARL, a simple yet effective reinforcement learning framework that encourages the generation of diverse answers within a controlled deviation range from the reference while preserving alignment with it. Our framework is fully compatible with existing general reinforcement learning methods and can be seamlessly integrated without additional verifiers. Extensive experiments on thirteen benchmarks demonstrate consistent improvements in reasoning performance. Notably, DARL surpasses RLPR, achieving average gains of 1.3 points on six reasoning benchmarks and 9.5 points on seven general benchmarks, highlighting its effectiveness in improving both reasoning accuracy and output diversity.

As agents based on large language models are increasingly deployed to long-horizon tasks, maintaining their alignment with stakeholder preferences becomes critical. Effective alignment in such settings requires reward models that are interpretable so that stakeholders can understand and audit model objectives. Moreover, reward models must be capable of steering agents at interaction time, allowing preference shifts to be incorporated without retraining. We introduce ARCANE, a framework that frames alignment as a multi-agent collaboration problem that dynamically represents stakeholder preferences as natural-language rubrics: weighted sets of verifiable criteria that can be generated on-the-fly from task context. Inspired by utility theory, we formulate rubric learning as a reconstruction problem and apply a regularized Group-Sequence Policy Optimization (GSPO) procedure that balances interpretability, faithfulness, and computational efficiency. Using a corpus of 219 labeled rubrics derived from the GDPVal benchmark, we evaluate ARCANE on challenging tasks requiring multi-step reasoning and tool use. The learned rubrics produce compact, legible evaluations and enable configurable trade-offs (e.g., correctness vs. conciseness) without retraining. Our results show that rubric-based reward models offer a promising path toward interpretable, test-time adaptive alignment for complex, long-horizon AI systems.

Large language models (LLMs) are increasingly trained with reinforcement learning from verifiable rewards (RLVR), yet real-world deployment demands models that can self-improve without labels or external judges. Existing label-free methods, confidence minimization, self-consistency, or majority-vote objectives, stabilize learning but steadily shrink exploration, causing an entropy collapse: generations become shorter, less diverse, and brittle. Unlike prior approaches such as Test-Time Reinforcement Learning (TTRL), which primarily adapt models to the immediate unlabeled dataset at hand, our goal is broader: to enable general improvements without sacrificing the model's inherent exploration capacity and generalization ability, i.e., evolving. We formalize this issue and propose EVolution-Oriented and Label-free Reinforcement Learning (EVOL-RL), a simple rule that couples stability with variation under a label-free setting. EVOL-RL keeps the majority-voted answer as a stable anchor (selection) while adding a novelty-aware reward that favors responses whose reasoning differs from what has already been produced (variation), measured in semantic space. Implemented with GRPO, EVOL-RL also uses asymmetric clipping to preserve strong signals and an entropy regularizer to sustain search. This majority-for-selection + novelty-for-variation design prevents collapse, maintains longer and more informative chains of thought, and improves both pass@1 and pass@n. EVOL-RL consistently outperforms the majority-only TTRL baseline; e.g., training on label-free AIME24 lifts Qwen3-4B-Base AIME25 pass@1 from TTRL's 4.6% to 16.4%, and pass@16 from 18.5% to 37.9%. EVOL-RL not only prevents diversity collapse but also unlocks stronger generalization across domains (e.g., GPQA). Furthermore, we demonstrate that EVOL-RL also boosts performance in the RLVR setting, highlighting its broad applicability.

Reinforcement learning (RL) offers a principled way to enhance the reasoning capabilities of large language models, yet its effectiveness hinges on training signals that remain informative as models evolve. In practice, RL progress often slows when task difficulty becomes poorly aligned with model capability, or when training is dominated by a narrow set of recurring problem patterns. To jointly address these issues, we propose SCALER (Synthetic sCalable Adaptive Learning Environment for Reasoning), a framework that sustains effective learning signals through adaptive environment design. SCALER introduces a scalable synthesis pipeline that converts real-world programming problems into verifiable reasoning environments with controllable difficulty and unbounded instance generation, enabling RL training beyond finite datasets while preserving strong correctness guarantees. Building on this, SCALER further employs an adaptive multi-environment RL strategy that dynamically adjusts instance difficulty and curates the active set of environments to track the model's capability frontier and maintain distributional diversity. This co-adaptation prevents reward sparsity, mitigates overfitting to narrow task patterns, and supports sustained improvement throughout training. Extensive experiments show that SCALER consistently outperforms dataset-based RL baselines across diverse reasoning benchmarks and exhibits more stable, long-horizon training dynamics.

Large language models (LLMs) have shown remarkable potential as autonomous agents, particularly in web-based tasks. However, existing LLM web agents heavily rely on expensive proprietary LLM APIs, while open LLMs lack the necessary decision-making capabilities. This paper introduces WebRL, a self-evolving online curriculum reinforcement learning framework designed to train high-performance web agents using open LLMs. WebRL addresses three key challenges in building LLM web agents, including the scarcity of training tasks, sparse feedback signals, and policy distribution drift in online learning. Specifically, WebRL incorporates 1) a self-evolving curriculum that generates new tasks from unsuccessful attempts, 2) a robust outcome-supervised reward model (ORM), and 3) adaptive reinforcement learning strategies to ensure consistent improvements. We apply WebRL to transform open Llama-3.1 and GLM-4 models into proficient web agents. On WebArena-Lite, WebRL improves the success rate of Llama-3.1-8B from 4.8% to 42.4%, and from 6.1% to 43% for GLM-4-9B. These open models significantly surpass the performance of GPT-4-Turbo (17.6%) and GPT-4o (13.9%) and outperform previous state-of-the-art web agents trained on open LLMs (AutoWebGLM, 18.2%). Our findings demonstrate WebRL's effectiveness in bridging the gap between open and proprietary LLM-based web agents, paving the way for more accessible and powerful autonomous web interaction systems.

This paper investigates Reinforcement Learning (RL) on data without explicit labels for reasoning tasks in Large Language Models (LLMs). The core challenge of the problem is reward estimation during inference while not having access to ground-truth information. While this setting appears elusive, we find that common practices in Test-Time Scaling (TTS), such as majority voting, yield surprisingly effective rewards suitable for driving RL training. In this work, we introduce Test-Time Reinforcement Learning (TTRL), a novel method for training LLMs using RL on unlabeled data. TTRL enables self-evolution of LLMs by utilizing the priors in the pre-trained models. Our experiments demonstrate that TTRL consistently improves performance across a variety of tasks and models. Notably, TTRL boosts the pass@1 performance of Qwen-2.5-Math-7B by approximately 159% on the AIME 2024 with only unlabeled test data. Furthermore, although TTRL is only supervised by the Maj@N metric, TTRL has demonstrated performance to consistently surpass the upper limit of the initial model, and approach the performance of models trained directly on test data with ground-truth labels. Our experimental findings validate the general effectiveness of TTRL across various tasks, and highlight TTRL's potential for broader tasks and domains. GitHub: https://github.com/PRIME-RL/TTRL

Reinforcement learning (RL) has proven effective for fine-tuning large language models (LLMs), significantly enhancing their reasoning abilities in domains such as mathematics and code generation. A crucial factor influencing RL fine-tuning success is the training curriculum: the order in which training problems are presented. While random curricula serve as common baselines, they remain suboptimal; manually designed curricula often rely heavily on heuristics, and online filtering methods can be computationally prohibitive. To address these limitations, we propose Self-Evolving Curriculum (SEC), an automatic curriculum learning method that learns a curriculum policy concurrently with the RL fine-tuning process. Our approach formulates curriculum selection as a non-stationary Multi-Armed Bandit problem, treating each problem category (e.g., difficulty level or problem type) as an individual arm. We leverage the absolute advantage from policy gradient methods as a proxy measure for immediate learning gain. At each training step, the curriculum policy selects categories to maximize this reward signal and is updated using the TD(0) method. Across three distinct reasoning domains: planning, inductive reasoning, and mathematics, our experiments demonstrate that SEC significantly improves models' reasoning capabilities, enabling better generalization to harder, out-of-distribution test problems. Additionally, our approach achieves better skill balance when fine-tuning simultaneously on multiple reasoning domains. These findings highlight SEC as a promising strategy for RL fine-tuning of LLMs.

We introduce rStar2-Agent, a 14B math reasoning model trained with agentic reinforcement learning to achieve frontier-level performance. Beyond current long CoT, the model demonstrates advanced cognitive behaviors, such as thinking carefully before using Python coding tools and reflecting on code execution feedback to autonomously explore, verify, and refine intermediate steps in complex problem-solving. This capability is enabled through three key innovations that makes agentic RL effective at scale: (i) an efficient RL infrastructure with a reliable Python code environment that supports high-throughput execution and mitigates the high rollout costs, enabling training on limited GPU resources (64 MI300X GPUs); (ii) GRPO-RoC, an agentic RL algorithm with a Resample-on-Correct rollout strategy that addresses the inherent environment noises from coding tools, allowing the model to reason more effectively in a code environment; (iii) An efficient agent training recipe that starts with non-reasoning SFT and progresses through multi-RL stages, yielding advanced cognitive abilities with minimal compute cost. To this end, rStar2-Agent boosts a pre-trained 14B model to state of the art in only 510 RL steps within one week, achieving average pass@1 scores of 80.6% on AIME24 and 69.8% on AIME25, surpassing DeepSeek-R1 (671B) with significantly shorter responses. Beyond mathematics, rStar2-Agent-14B also demonstrates strong generalization to alignment, scientific reasoning, and agentic tool-use tasks. Code and training recipes are available at https://github.com/microsoft/rStar.

We propose RLAnything, a reinforcement learning framework that dynamically forges environment, policy, and reward models through closed-loop optimization, amplifying learning signals and strengthening the overall RL system for any LLM or agentic scenarios. Specifically, the policy is trained with integrated feedback from step-wise and outcome signals, while the reward model is jointly optimized via consistency feedback, which in turn further improves policy training. Moreover, our theory-motivated automatic environment adaptation improves training for both the reward and policy models by leveraging critic feedback from each, enabling learning from experience. Empirically, each added component consistently improves the overall system, and RLAnything yields substantial gains across various representative LLM and agentic tasks, boosting Qwen3-VL-8B-Thinking by 9.1% on OSWorld and Qwen2.5-7B-Instruct by 18.7% and 11.9% on AlfWorld and LiveBench, respectively. We also that optimized reward-model signals outperform outcomes that rely on human labels. Code: https://github.com/Gen-Verse/Open-AgentRL

Reinforcement Learning (RL) has emerged as a transformative approach for aligning and enhancing Large Language Models (LLMs), addressing critical challenges in instruction following, ethical alignment, and reasoning capabilities. This survey offers a comprehensive foundation on the integration of RL with language models, highlighting prominent algorithms such as Proximal Policy Optimization (PPO), Q-Learning, and Actor-Critic methods. Additionally, it provides an extensive technical overview of RL techniques specifically tailored for LLMs, including foundational methods like Reinforcement Learning from Human Feedback (RLHF) and AI Feedback (RLAIF), as well as advanced strategies such as Direct Preference Optimization (DPO) and Group Relative Policy Optimization (GRPO). We systematically analyze their applications across domains, i.e., from code generation to tool-augmented reasoning. We also present a comparative taxonomy based on reward modeling, feedback mechanisms, and optimization strategies. Our evaluation highlights key trends. RLHF remains dominant for alignment, and outcome-based RL such as RLVR significantly improves stepwise reasoning. However, persistent challenges such as reward hacking, computational costs, and scalable feedback collection underscore the need for continued innovation. We further discuss emerging directions, including hybrid RL algorithms, verifier-guided training, and multi-objective alignment frameworks. This survey serves as a roadmap for researchers advancing RL-driven LLM development, balancing capability enhancement with safety and scalability.

Reinforcement learning (RL) has become a powerful approach for improving the reasoning capabilities of large language models (LLMs), as evidenced by recent successes such as OpenAI's o1 and Deepseek-R1. However, applying RL at scale remains intimidatingly resource-intensive, requiring multiple model copies and extensive GPU workloads. On the other hand, while being powerful, recent studies suggest that RL does not fundamentally endow models with new knowledge; rather, it primarily reshapes the model's output distribution to activate reasoning capabilities latent in the base model. Building on this insight, we hypothesize that the changes in output probabilities induced by RL are largely model-size invariant, opening the door to a more efficient paradigm: training a small model with RL and transferring its induced probability shifts to larger base models. To verify our hypothesis, we conduct a token-level analysis of decoding trajectories and find high alignment in RL-induced output distributions across model scales, validating our hypothesis. Motivated by this, we propose RAST, a simple yet effective method that transfers reasoning behaviors by injecting RL-induced probability adjustments from a small RL-trained model into larger models. Experiments across multiple mathematical reasoning benchmarks show that RAST substantially and consistently enhances the reasoning capabilities of base models while requiring significantly lower GPU memory than direct RL training, sometimes even yielding better performance than the RL-trained counterparts. Our findings offer new insights into the nature of RL-driven reasoning and practical strategies for scaling its benefits without incurring its full computational cost. The project page of RAST is available at https://ozyyshr.github.io/RAST/.

Reinforcement learning has been applied in operation research and has shown promise in solving large combinatorial optimization problems. However, existing works focus on developing neural network architectures for certain problems. These works lack the flexibility to incorporate recent advances in reinforcement learning, as well as the flexibility of customizing model architectures for operation research problems. In this work, we analyze the end-to-end autoregressive models for vehicle routing problems and show that these models can benefit from the recent advances in reinforcement learning with a careful re-implementation of the model architecture. In particular, we re-implemented the Attention Model and trained it with Proximal Policy Optimization (PPO) in CleanRL, showing at least 8 times speed up in training time. We hereby introduce RLOR, a flexible framework for Deep Reinforcement Learning for Operation Research. We believe that a flexible framework is key to developing deep reinforcement learning models for operation research problems. The code of our work is publicly available at https://github.com/cpwan/RLOR.

Preference-based reinforcement learning (PbRL) is an approach that enables RL agents to learn from preference, which is particularly useful when formulating a reward function is challenging. Existing PbRL methods generally involve a two-step procedure: they first learn a reward model based on given preference data and then employ off-the-shelf reinforcement learning algorithms using the learned reward model. However, obtaining an accurate reward model solely from preference information, especially when the preference is from human teachers, can be difficult. Instead, we propose a PbRL algorithm that directly learns from preference without requiring any reward modeling. To achieve this, we adopt a contrastive learning framework to design a novel policy scoring metric that assigns a high score to policies that align with the given preferences. We apply our algorithm to offline RL tasks with actual human preference labels and show that our algorithm outperforms or is on par with the existing PbRL methods. Notably, on high-dimensional control tasks, our algorithm surpasses offline RL methods that learn with ground-truth reward information. Finally, we show that our algorithm can be successfully applied to fine-tune large language models.

Reinforcement learning drives recent advances in LLM reasoning and agentic capabilities, yet current approaches struggle with both exploration and exploitation. Exploration suffers from low success rates on difficult tasks and high costs of repeated rollouts from scratch. Exploitation suffers from coarse credit assignment and training instability: Trajectory-level rewards penalize valid prefixes for later errors, and failure-dominated groups overwhelm the few positive signals, leaving optimization without constructive direction. To this end, we propose R^3L, Reflect-then-Retry Reinforcement Learning with Language-Guided Exploration, Pivotal Credit, and Positive Amplification. To synthesize high-quality trajectories, R^3L shifts from stochastic sampling to active synthesis via reflect-then-retry, leveraging language feedback to diagnose errors, transform failed attempts into successful ones, and reduce rollout costs by restarting from identified failure points. With errors diagnosed and localized, Pivotal Credit Assignment updates only the diverging suffix where contrastive signals exist, excluding the shared prefix from gradient update. Since failures dominate on difficult tasks and reflect-then-retry produces off-policy data, risking training instability, Positive Amplification upweights successful trajectories to ensure positive signals guide the optimization process. Experiments on agentic and reasoning tasks demonstrate 5\% to 52\% relative improvements over baselines while maintaining training stability. Our code is released at https://github.com/shiweijiezero/R3L.

Reinforcement learning (RL) is a framework for solving sequential decision-making problems. In this work, we demonstrate that, surprisingly, RL emerges during the inference time of large language models (LLMs), a phenomenon we term in-context RL (ICRL). To reveal this capability, we introduce a simple multi-round prompting framework, we call ICRL prompting, for inference-time self-improvement. The goal of ICRL prompting is to guide LLMs to perform reinforcement learning during inference for self-improvement on a given task. After each response, the model receives numerical scalar feedback, denoted as a reward. In the next round, we prompt the LLM again together with a context that concatenates all prior responses and their associated rewards. We consistently observe that response quality improves as the context grows. In other words, the LLM can optimize scalar reward signals during inference, exhibiting behavior analogous to reinforcement learning. We evaluate ICRL prompting on Game of 24, creative writing, ScienceWorld, and Olympiad-level math competitions (AIME and HMMT), demonstrating significant improvements over baselines such as Self-Refine and Reflexion. Notably, even when the reward signals are generated by the same LLM, ICRL prompting still improves performance, highlighting a promising new paradigm for test-time scaling.

Building agentic systems that can autonomously self-improve from experience is a longstanding goal of AI. Large language models (LLMs) today primarily self-improve via two mechanisms: self-reflection for context updates, and reinforcement learning (RL) for weight updates. In this work, we propose Evolutionary System Prompt Learning (E-SPL), a method for jointly improving model contexts and model weights. In each RL iteration, E-SPL samples trajectories under multiple system prompts in parallel, then jointly applies RL updates to LLM weights and evolutionary updates to system prompts. System prompts evolve via mutation and crossover, two genetic operators driven by LLM self-reflection; selection is based on relative performance ratings updated across RL iterations. E-SPL encourages a natural division between declarative knowledge encoded in prompts and procedural knowledge encoded in weights, resulting in improved performance across reasoning and agentic tasks. For instance, in an easy-to-hard (AIME rightarrow BeyondAIME) generalization setting, E-SPL improves RL success rate from 38.8% rightarrow 45.1% while also outperforming reflective prompt evolution (40.0%). Overall, our results demonstrate that RL and system prompt evolution are deeply synergistic, and combining the two yields consistent gains in sample efficiency and generalization. Code: https://github.com/LunjunZhang/E-SPL

Reinforcement learning (RL) provides a principled framework for improving Vision-Language Models (VLMs) on complex reasoning tasks. However, existing RL approaches often rely on human-annotated labels or task-specific heuristics to define verifiable rewards, both of which are costly and difficult to scale. We introduce VisPlay, a self-evolving RL framework that enables VLMs to autonomously improve their reasoning abilities using large amounts of unlabeled image data. Starting from a single base VLM, VisPlay assigns the model into two interacting roles: an Image-Conditioned Questioner that formulates challenging yet answerable visual questions, and a Multimodal Reasoner that generates silver responses. These roles are jointly trained with Group Relative Policy Optimization (GRPO), which incorporates diversity and difficulty rewards to balance the complexity of generated questions with the quality of the silver answers. VisPlay scales efficiently across two model families. When trained on Qwen2.5-VL and MiMo-VL, VisPlay achieves consistent improvements in visual reasoning, compositional generalization, and hallucination reduction across eight benchmarks, including MM-Vet and MMMU, demonstrating a scalable path toward self-evolving multimodal intelligence. The project page is available at https://bruno686.github.io/VisPlay/

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced the reasoning capabilities of Large Language Models (LLMs). However, methods such as GRPO and DAPO suffer from substantial computational cost, since they rely on sampling many rollouts for each prompt. Moreover, in RLVR the relative advantage is often sparse: many samples become nearly all-correct or all-incorrect, yielding low within-group reward variance and thus weak learning signals. In this paper, we introduce arrol (Accelerating RLVR via online Rollout Pruning), an online rollout pruning method that prunes rollouts during generation while explicitly steering the surviving ones more correctness-balanced to enhance learning signals. Specifically, arrol trains a lightweight quality head on-the-fly to predict the success probability of partial rollouts and uses it to make early pruning decisions. The learned quality head can further weigh candidates to improve inference accuracy during test-time scaling. To improve efficiency, we present a system design that prunes rollouts inside the inference engine and re-batches the remaining ones for log-probability computation and policy updates. Across GRPO and DAPO on Qwen-3 and LLaMA-3.2 models (1B-8B), arrol improves average accuracy by +2.30 to +2.99 while achieving up to 1.7x training speedup, and yielding up to +8.33 additional gains in average accuracy in test-time scaling. The code is available at https://github.com/Hsu1023/ARRoL.

Reinforcement learning (RL) has been widely used in training large language models~(LLMs) for preventing unexpected outputs, \eg reducing harmfulness and errors. However, existing RL methods mostly adopt the instance-level reward, which is unable to provide fine-grained supervision for complex reasoning tasks, and can not focus on the few key tokens that lead to the incorrectness. To address it, we propose a new RL method named RLMEC that incorporates a generative model as the reward model, which is trained by the erroneous solution rewriting task under the minimum editing constraint, and can produce token-level rewards for RL training. Based on the generative reward model, we design the token-level RL objective for training and an imitation-based regularization for stabilizing RL process. And the both objectives focus on the learning of the key tokens for the erroneous solution, reducing the effect of other unimportant tokens. The experiment results on mathematical tasks and question-answering tasks have demonstrated the effectiveness of our approach. Our code and data are available at https://github.com/RUCAIBox/RLMEC.

Reinforcement learning (RL) has enabled the training of large language model (LLM) agents to interact with the environment and to solve multi-turn long-horizon tasks. However, the RL-trained agents often struggle in tasks that require active exploration and fail to efficiently adapt from trial-and-error experiences. In this paper, we present LaMer, a general Meta-RL framework that enables LLM agents to actively explore and learn from the environment feedback at test time. LaMer consists of two key components: (i) a cross-episode training framework to encourage exploration and long-term rewards optimization; and (ii) in-context policy adaptation via reflection, allowing the agent to adapt their policy from task feedback signal without gradient update. Experiments across diverse environments show that LaMer significantly improves performance over RL baselines, with 11%, 14%, and 19% performance gains on Sokoban, MineSweeper and Webshop, respectively. Moreover, LaMer also demonstrates better generalization to more challenging or previously unseen tasks compared to the RL-trained agents. Overall, our results demonstrate that Meta-RL provides a principled approach to induce exploration in language agents, enabling more robust adaptation to novel environments through learned exploration strategies.

Reinforcement learning (RL) is a powerful way to adapt foundation models to specialized tasks, but its reliance on large-scale human-labeled data limits broad adoption. We introduce Synthetic Data RL, a simple and general framework that reinforcement fine-tunes models using only synthetic data generated from a task definition. Our method first generates question and answer pairs from the task definition and retrieved documents, then adapts the difficulty of the question based on model solvability, and selects questions using the average pass rate of the model across samples for RL training. On Qwen-2.5-7B, our method achieves a 29.2% absolute improvement over the base model on GSM8K (+2.9 pp vs. instruction-tuned, +6.6 pp vs. Self-Instruct), 8.7% on MATH, 13.1% on GPQA (+7.0 pp vs. SynthLLM), 8.9% on MedQA, 17.7% on CQA (law) and 13.7% on CFA (finance). It surpasses supervised fine-tuning under the same data budget and nearly matches RL with full human data across datasets (e.g., +17.2 pp on GSM8K). Adding 100 human demonstrations improves the performance of GSM8K only by 0.4 pp, showing a limited added value. By reducing human data annotation, Synthetic Data RL enables scalable and efficient RL-based model adaptation. Code and demos are available at https://github.com/gydpku/Data_Synthesis_RL/.

Reinforcement learning (RL) has emerged as the de-facto paradigm for improving the reasoning capabilities of large language models (LLMs). We have developed RLAX, a scalable RL framework on TPUs. RLAX employs a parameter-server architecture. A master trainer periodically pushes updated model weights to the parameter server while a fleet of inference workers pull the latest weights and generates new rollouts. We introduce a suite of system techniques to enable scalable and preemptible RL for a diverse set of state-of-art RL algorithms. To accelerate convergence and improve model quality, we have devised new dataset curation and alignment techniques. Large-scale evaluations show that RLAX improves QwQ-32B's pass@8 accuracy by 12.8% in just 12 hours 48 minutes on 1024 v5p TPUs, while remaining robust to preemptions during training.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key ingredient for unlocking complex reasoning capabilities in large language models. Recent work ProRL has shown promise in scaling RL by increasing the number of training steps. However, performance plateaus after thousands of steps, with clear diminishing returns from allocating more computation to additional training. In this work, we investigate a complementary paradigm for scaling RL, BroR-Lincreasing the number of rollouts per example to hundreds to exhaustively Broaden exploration, which yields continuous performance gains beyond the saturation point observed in ProRL when scaling the number of training steps. Our approach is motivated by a mass balance equation analysis allowing us to characterize the rate of change in probability mass for correct and incorrect tokens during the reinforcement process. We show that under a one-step RL assumption, sampled rollout tokens always contribute to correct-mass expansion, while unsampled tokens outside rollouts may lead to gains or losses depending on their distribution and the net reward balance. Importantly, as the number of rollouts per example N increases, the effect of unsampled terms diminishes, ensuring overall correct-mass expansion. To validate our theoretical analysis, we conduct simulations under more relaxed conditions and find that a sufficiently large rollout size N-corresponding to ample exploration-guarantees an increase in the probability mass of all correct tokens. Empirically, BroRL revives models saturated after 3K ProRL training steps and demonstrates robust, continuous improvement, achieving state-of-the-art results for the 1.5B model across diverse benchmarks.

Reinforcement learning (RL) problems can be challenging without well-shaped rewards. Prior work on provably efficient RL methods generally proposes to address this issue with dedicated exploration strategies. However, another way to tackle this challenge is to reformulate it as a multi-task RL problem, where the task space contains not only the challenging task of interest but also easier tasks that implicitly function as a curriculum. Such a reformulation opens up the possibility of running existing multi-task RL methods as a more efficient alternative to solving a single challenging task from scratch. In this work, we provide a theoretical framework that reformulates a single-task RL problem as a multi-task RL problem defined by a curriculum. Under mild regularity conditions on the curriculum, we show that sequentially solving each task in the multi-task RL problem is more computationally efficient than solving the original single-task problem, without any explicit exploration bonuses or other exploration strategies. We also show that our theoretical insights can be translated into an effective practical learning algorithm that can accelerate curriculum learning on simulated robotic tasks.

Reinforcement learning for LLM reasoning has rapidly emerged as a prominent research area, marked by a significant surge in related studies on both algorithmic innovations and practical applications. Despite this progress, several critical challenges remain, including the absence of standardized guidelines for employing RL techniques and a fragmented understanding of their underlying mechanisms. Additionally, inconsistent experimental settings, variations in training data, and differences in model initialization have led to conflicting conclusions, obscuring the key characteristics of these techniques and creating confusion among practitioners when selecting appropriate techniques. This paper systematically reviews widely adopted RL techniques through rigorous reproductions and isolated evaluations within a unified open-source framework. We analyze the internal mechanisms, applicable scenarios, and core principles of each technique through fine-grained experiments, including datasets of varying difficulty, model sizes, and architectures. Based on these insights, we present clear guidelines for selecting RL techniques tailored to specific setups, and provide a reliable roadmap for practitioners navigating the RL for the LLM domain. Finally, we reveal that a minimalist combination of two techniques can unlock the learning capability of critic-free policies using vanilla PPO loss. The results demonstrate that our simple combination consistently improves performance, surpassing strategies like GRPO and DAPO.

Reinforcement learning (RL) has become an effective approach for fine-tuning large language models (LLMs), particularly to enhance their reasoning capabilities. However, RL fine-tuning remains highly resource-intensive, and existing work has largely overlooked the problem of data efficiency. In this paper, we propose two techniques to improve data efficiency in LLM RL fine-tuning: difficulty-targeted online data selection and rollout replay. We introduce the notion of adaptive difficulty to guide online data selection, prioritizing questions of moderate difficulty that are more likely to yield informative learning signals. To estimate adaptive difficulty efficiently, we develop an attention-based framework that requires rollouts for only a small reference set of questions. The adaptive difficulty of the remaining questions is then estimated based on their similarity to this set. To further reduce rollout cost, we introduce a rollout replay mechanism inspired by experience replay in traditional RL. This technique reuses recent rollouts, lowering per-step computation while maintaining stable updates. Experiments across 6 LLM-dataset combinations show that our method reduces RL fine-tuning time by 23% to 62% while reaching the same level of performance as the original GRPO algorithm. Our code is available at https://github.com/ASTRAL-Group/data-efficient-llm-rl.

Large reasoning models (LRMs) aim to solve diverse and complex problems through structured reasoning. Recent advances in group-based policy optimization methods have shown promise in enabling stable advantage estimation without reliance on process-level annotations. However, these methods rely on advantage gaps induced by high-quality samples within the same batch, which makes the training process fragile and inefficient when intra-group advantages collapse under challenging tasks. To address these problems, we propose a reinforcement learning mechanism named \textbf{R^3} that along three directions: (1) a cross-context \underline{\textbf{R}eplay} strategy that maintains the intra-group advantage by recalling valuable examples from historical trajectories of the same query, (2) an in-context self-\underline{\textbf{R}eflection} mechanism enabling models to refine outputs by leveraging past failures, and (3) a structural entropy \underline{\textbf{R}anking reward}, which assigns relative rewards to truncated or failed samples by ranking responses based on token-level entropy patterns, capturing both local exploration and global stability. We implement our method on Deepseek-R1-Distill-Qwen-1.5B and train it on the DeepscaleR-40k in the math domain. Experiments demonstrate our method achieves SoTA performance on several math benchmarks, representing significant improvements and fewer reasoning tokens over the base models. Code and model will be released.

Large Language Models (LLMs) trained via Reinforcement Learning (RL) have exhibited strong reasoning capabilities and emergent reflective behaviors, such as backtracking and error correction. However, conventional Markovian RL confines exploration to the training phase to learn an optimal deterministic policy and depends on the history contexts only through the current state. Therefore, it remains unclear whether reflective reasoning will emerge during Markovian RL training, or why they are beneficial at test time. To remedy this, we recast reflective exploration within the Bayes-Adaptive RL framework, which explicitly optimizes the expected return under a posterior distribution over Markov decision processes. This Bayesian formulation inherently incentivizes both reward-maximizing exploitation and information-gathering exploration via belief updates. Our resulting algorithm, BARL, instructs the LLM to stitch and switch strategies based on the observed outcomes, offering principled guidance on when and how the model should reflectively explore. Empirical results on both synthetic and mathematical reasoning tasks demonstrate that BARL outperforms standard Markovian RL approaches at test time, achieving superior token efficiency with improved exploration effectiveness. Our code is available at https://github.com/shenao-zhang/BARL.

Recent advances in reasoning-centric language models have highlighted reinforcement learning (RL) as a promising method for aligning models with verifiable rewards. However, it remains contentious whether RL truly expands a model's reasoning capabilities or merely amplifies high-reward outputs already latent in the base model's distribution, and whether continually scaling up RL compute reliably leads to improved reasoning performance. In this work, we challenge prevailing assumptions by demonstrating that prolonged RL (ProRL) training can uncover novel reasoning strategies that are inaccessible to base models, even under extensive sampling. We introduce ProRL, a novel training methodology that incorporates KL divergence control, reference policy resetting, and a diverse suite of tasks. Our empirical analysis reveals that RL-trained models consistently outperform base models across a wide range of pass@k evaluations, including scenarios where base models fail entirely regardless of the number of attempts. We further show that reasoning boundary improvements correlates strongly with task competence of base model and training duration, suggesting that RL can explore and populate new regions of solution space over time. These findings offer new insights into the conditions under which RL meaningfully expands reasoning boundaries in language models and establish a foundation for future work on long-horizon RL for reasoning. We release model weights to support further research: https://huggingface.co/nvidia/Nemotron-Research-Reasoning-Qwen-1.5B

We introduce Reinforcement Learning (RL) with Adaptive Verifiable Environments (RLVE), an approach using verifiable environments that procedurally generate problems and provide algorithmically verifiable rewards, to scale up RL for language models (LMs). RLVE enables each verifiable environment to dynamically adapt its problem difficulty distribution to the policy model's capabilities as training progresses. In contrast, static data distributions often lead to vanishing learning signals when problems are either too easy or too hard for the policy. To implement RLVE, we create RLVE-Gym, a large-scale suite of 400 verifiable environments carefully developed through manual environment engineering. Using RLVE-Gym, we show that environment scaling, i.e., expanding the collection of training environments, consistently improves generalizable reasoning capabilities. RLVE with joint training across all 400 environments in RLVE-Gym yields a 3.37% absolute average improvement across six reasoning benchmarks, starting from one of the strongest 1.5B reasoning LMs. By comparison, continuing this LM's original RL training yields only a 0.49% average absolute gain despite using over 3x more compute. We release our code publicly.

Policy-based reinforcement learning currently plays an important role in improving LLMs on mathematical reasoning tasks. However, existing rollout-based reinforcement learning methods (GRPO, DAPO, GSPO, etc.) fail to explicitly consider LLMs' learning ability for samples of different difficulty levels, which is contrary to the human cognitive process of mathematical reasoning tasks from easy to difficult. Intuitively, we find that the variance of the rollout group's reward in RLVR partly reflects the difficulty of the current sample for LLMs. Samples that are too easy or too difficult have a lower variance, while samples with moderate difficulty have a higher variance. Based on this, we propose VCRL, a curriculum reinforcement learning framework that dynamically controls the difficulty of training samples based on the variance of group rewards. Experiments on five mathematical benchmarks and two models reveal the advantages of VCRL over the current LLM RL baselines.

We propose Dynamic Rank Reinforcement Learning (DR-RL), a novel framework that adaptively optimizes the low-rank factorization of Multi-Head Self-Attention (MHSA) in Large Language Models (LLMs) through the integration of reinforcement learning and online matrix perturbation theory. While traditional low-rank approximations often rely on static rank assumptions--limiting their flexibility across diverse input contexts--our method dynamically selects ranks based on real-time sequence dynamics, layer-specific sensitivities, and hardware constraints. The core innovation lies in an RL agent that formulates rank selection as a sequential policy optimization problem, where the reward function strictly balances attention fidelity against computational latency. Crucially, we employ online matrix perturbation bounds to enable incremental rank updates, thereby avoiding the prohibitive cost of full decomposition during inference. Furthermore, the integration of a lightweight Transformer-based policy network and batched Singular Value Decomposition (SVD) operations ensures scalable deployment on modern GPU architectures. Experiments demonstrate that DR-RL maintains downstream accuracy statistically equivalent to full-rank attention while significantly reducing Floating Point Operations (FLOPs), particularly in long-sequence regimes (L > 4096). This work bridges the gap between adaptive efficiency and theoretical rigor in MHSA, offering a principled, mathematically grounded alternative to heuristic rank reduction techniques in resource-constrained deep learning. Source code and experiment logs are available at: https://github.com/canererden/DR_RL_Project

Outcome-reward reinforcement learning (RL) is a common and increasingly significant way to refine the step-by-step reasoning of multimodal large language models (MLLMs). In the multiple-choice setting - a dominant format for multimodal reasoning benchmarks - the paradigm faces a significant yet often overlooked obstacle: unfaithful trajectories that guess the correct option after a faulty chain of thought receive the same reward as genuine reasoning, which is a flaw that cannot be ignored. We propose Self-Consistency Sampling (SCS) to correct this issue. For each question, SCS (i) introduces small visual perturbations and (ii) performs repeated truncation and resampling of an initial trajectory; agreement among the resulting trajectories yields a differentiable consistency score that down-weights unreliable traces during policy updates. Based on Qwen2.5-VL-7B-Instruct, plugging SCS into RLOO, GRPO, and REINFORCE++ series improves accuracy by up to 7.7 percentage points on six multimodal benchmarks with negligible extra computation. SCS also yields notable gains on both Qwen2.5-VL-3B-Instruct and InternVL3-8B, offering a simple, general remedy for outcome-reward RL in MLLMs.

While Reinforcement Learning ( RL) has made great strides towards solving increasingly complicated problems, many algorithms are still brittle to even slight environmental changes. Contextual Reinforcement Learning (cRL) provides a framework to model such changes in a principled manner, thereby enabling flexible, precise and interpretable task specification and generation. Our goal is to show how the framework of cRL contributes to improving zero-shot generalization in RL through meaningful benchmarks and structured reasoning about generalization tasks. We confirm the insight that optimal behavior in cRL requires context information, as in other related areas of partial observability. To empirically validate this in the cRL framework, we provide various context-extended versions of common RL environments. They are part of the first benchmark library, CARL, designed for generalization based on cRL extensions of popular benchmarks, which we propose as a testbed to further study general agents. We show that in the contextual setting, even simple RL environments become challenging - and that naive solutions are not enough to generalize across complex context spaces.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs) on reasoning tasks that elicit emergent long chains of thought (CoTs). Unlike supervised learning, it updates the model using both correct and incorrect samples via policy gradients. To better understand its mechanism, we decompose the learning signal into reinforcing correct responses and penalizing incorrect ones, referred to as Positive and Negative Sample Reinforcement (PSR and NSR), respectively. We train Qwen2.5-Math-7B and Qwen3-4B on a mathematical reasoning dataset and uncover a surprising result: training with only negative samples -- without reinforcing correct responses -- can be highly effective: it consistently improves performance over the base model across the entire Pass@k spectrum (k up to 256), often matching or surpassing PPO and GRPO. In contrast, reinforcing only correct responses improves Pass@1 but degrades performance at higher k, due to reduced diversity. These inference-scaling trends highlight that solely penalizing incorrect responses may contribute more to performance than previously recognized. Through gradient analysis, we show that NSR works by suppressing incorrect generations and redistributing probability mass toward other plausible candidates, guided by the model's prior beliefs. It refines the model's existing knowledge rather than introducing entirely new behaviors. Building on this insight, we propose a simple variant of the RL objective that upweights NSR, and show that it consistently improves overall Pass@k performance on MATH, AIME 2025, and AMC23. Our code is available at https://github.com/TianHongZXY/RLVR-Decomposed.

Existing agents for solving tasks such as ML engineering rely on prompting powerful language models. As a result, these agents do not improve with more experience. In this paper, we show that agents backed by weaker models that improve via reinforcement learning (RL) can outperform agents backed by much larger, but static models. We identify two major challenges with RL in this setting. First, actions can take a variable amount of time (e.g., executing code for different solutions), which leads to asynchronous policy gradient updates that favor faster but suboptimal solutions. To tackle variable-duration actions, we propose duration-aware gradient updates in a distributed asynchronous RL framework to amplify high-cost but high-reward actions. Second, using only test split performance as a reward provides limited feedback. A program that is nearly correct is treated the same as one that fails entirely. To address this, we propose environment instrumentation to offer partial credit, distinguishing almost-correct programs from those that fail early (e.g., during data loading). Environment instrumentation uses a separate static language model to insert print statement to an existing program to log the agent's experimental progress, from which partial credit can be extracted as reward signals for learning. Our experimental results on MLEBench suggest that performing gradient updates on a much smaller model (Qwen2.5-3B) trained with RL outperforms prompting a much larger model (Claude-3.5-Sonnet) with agent scaffolds, by an average of 22% across 12 Kaggle tasks.

While reinforcement learning (RL) has demonstrated remarkable success in enhancing large language models (LLMs), it has primarily focused on single-turn tasks such as solving math problems. Training effective web agents for multi-turn interactions remains challenging due to the complexity of long-horizon decision-making across dynamic web interfaces. In this work, we present WebAgent-R1, a simple yet effective end-to-end multi-turn RL framework for training web agents. It learns directly from online interactions with web environments by asynchronously generating diverse trajectories, entirely guided by binary rewards depending on task success. Experiments on the WebArena-Lite benchmark demonstrate the effectiveness of WebAgent-R1, boosting the task success rate of Qwen-2.5-3B from 6.1% to 33.9% and Llama-3.1-8B from 8.5% to 44.8%, significantly outperforming existing state-of-the-art methods and strong proprietary models such as OpenAI o3. In-depth analyses reveal the effectiveness of the thinking-based prompting strategy and test-time scaling through increased interactions for web tasks. We further investigate different RL initialization policies by introducing two variants, namely WebAgent-R1-Zero and WebAgent-R1-CoT, which highlight the importance of the warm-up training stage (i.e., behavior cloning) and provide insights on incorporating long chain-of-thought (CoT) reasoning in web agents.

Reinforcement learning has become a cornerstone for enhancing the reasoning capabilities of Large Language Models, where group-based approaches such as GRPO have emerged as efficient paradigms that optimize policies by leveraging intra-group performance differences. However, these methods typically rely on absolute numerical rewards, introducing intrinsic limitations. In verifiable tasks, identical group evaluations often result in sparse supervision, while in open-ended scenarios, the score range instability of reward models undermines advantage estimation based on group means. To address these limitations, we propose Reinforcement Learning with Relative Rewards (RLRR), a framework that shifts reward shaping from absolute scoring to relative ranking. Complementing this framework, we introduce the Ranking Reward Model, a listwise preference model tailored for group-based optimization to directly generate relative rankings. By transforming raw evaluations into robust relative signals, RLRR effectively mitigates signal sparsity and reward instability. Experimental results demonstrate that RLRR yields consistent performance improvements over standard group-based baselines across reasoning benchmarks and open-ended generation tasks.

The ever-growing complexity of reinforcement learning (RL) tasks demands a distributed RL system to efficiently generate and process a massive amount of data to train intelligent agents. However, existing open-source libraries suffer from various limitations, which impede their practical use in challenging scenarios where large-scale training is necessary. While industrial systems from OpenAI and DeepMind have achieved successful large-scale RL training, their system architecture and implementation details remain undisclosed to the community. In this paper, we present a novel abstraction on the dataflows of RL training, which unifies practical RL training across diverse applications into a general framework and enables fine-grained optimizations. Following this abstraction, we develop a scalable, efficient, and extensible distributed RL system called ReaLly Scalable RL (SRL). The system architecture of SRL separates major RL computation components and allows massively parallelized training. Moreover, SRL offers user-friendly and extensible interfaces for customized algorithms. Our evaluation shows that SRL outperforms existing academic libraries in both a single machine and a medium-sized cluster. In a large-scale cluster, the novel architecture of SRL leads to up to 3.7x speedup compared to the design choices adopted by the existing libraries. We also conduct a direct benchmark comparison to OpenAI's industrial system, Rapid, in the challenging hide-and-seek environment. SRL reproduces the same solution as reported by OpenAI with up to 5x speedup in wall-clock time. Furthermore, we also examine the performance of SRL in a much harder variant of the hide-and-seek environment and achieve substantial learning speedup by scaling SRL to over 15k CPU cores and 32 A100 GPUs. Notably, SRL is the first in the academic community to perform RL experiments at such a large scale.

Reinforcement learning with verifiable rewards (RLVR) has achieved remarkable success in enhancing the reasoning capabilities of large language models (LLMs). However, existing RLVR methods often suffer from exploration inefficiency due to mismatches between the training data's difficulty and the model's capability. LLMs fail to discover viable reasoning paths when problems are overly difficult, while learning little new capability when problems are too simple. In this work, we formalize the impact of problem difficulty by quantifying the relationship between loss descent speed and rollout accuracy. Building on this analysis, we propose SEELE, a novel supervision-aided RLVR framework that dynamically adjusts problem difficulty to stay within the high-efficiency region. SEELE augments each training sample by appending a hint (part of a full solution) after the original problem. Unlike previous hint-based approaches, SEELE deliberately and adaptively adjusts the hint length for each problem to achieve an optimal difficulty. To determine the optimal hint length, SEELE employs a multi-round rollout sampling strategy. In each round, it fits an item response theory model to the accuracy-hint pairs collected in preceding rounds to predict the required hint length for the next round. This instance-level, real-time difficulty adjustment aligns problem difficulty with the evolving model capability, thereby improving exploration efficiency. Experimental results show that SEELE outperforms Group Relative Policy Optimization (GRPO) and Supervised Fine-tuning (SFT) by +11.8 and +10.5 points, respectively, and surpasses the best previous supervision-aided approach by +3.6 points on average across six math reasoning benchmarks.

Reinforcement learning (RL) has emerged as an effective post-training paradigm for enhancing the reasoning capabilities of multimodal large language model (MLLM). However, current RL pipelines often suffer from training inefficiencies caused by two underexplored issues: Advantage Collapsing, where most advantages in a batch concentrate near zero, and Rollout Silencing, where the proportion of rollouts contributing non-zero gradients diminishes over time. These issues lead to suboptimal gradient updates and hinder long-term learning efficiency. To address these issues, we propose Shuffle-R1, a simple yet principled framework that improves RL fine-tuning efficiency by dynamically restructuring trajectory sampling and batch composition. It introduces (1) Pairwise Trajectory Sampling, which selects high-contrast trajectories with large advantages to improve gradient signal quality, and (2) Advantage-based Trajectory Shuffle, which increases exposure of valuable rollouts through informed batch reshuffling. Experiments across multiple reasoning benchmarks show that our framework consistently outperforms strong RL baselines with minimal overhead. These results highlight the importance of data-centric adaptations for more efficient RL training in MLLM.

Reinforcement learning (RL), earlier proven to be effective in large language and multi-modal models, has been successfully extended to enhance 2D image generation recently. However, applying RL to 3D generation remains largely unexplored due to the higher spatial complexity of 3D objects, which require globally consistent geometry and fine-grained local textures. This makes 3D generation significantly sensitive to reward designs and RL algorithms. To address these challenges, we conduct the first systematic study of RL for text-to-3D autoregressive generation across several dimensions. (1) Reward designs: We evaluate reward dimensions and model choices, showing that alignment with human preference is crucial, and that general multi-modal models provide robust signal for 3D attributes. (2) RL algorithms: We study GRPO variants, highlighting the effectiveness of token-level optimization, and further investigate the scaling of training data and iterations. (3) Text-to-3D Benchmarks: Since existing benchmarks fail to measure implicit reasoning abilities in 3D generation models, we introduce MME-3DR. (4) Advanced RL paradigms: Motivated by the natural hierarchy of 3D generation, we propose Hi-GRPO, which optimizes the global-to-local hierarchical 3D generation through dedicated reward ensembles. Based on these insights, we develop AR3D-R1, the first RL-enhanced text-to-3D model, expert from coarse shape to texture refinement. We hope this study provides insights into RL-driven reasoning for 3D generation. Code is released at https://github.com/Ivan-Tang-3D/3DGen-R1.

Recent progress in large language models (LLMs) has been propelled by reinforcement learning with verifiable rewards (RLVR) and test-time scaling. However, the limited output length of LLMs constrains the depth of reasoning attainable in a single inference process. Multi-agent reasoning systems offer a promising alternative by employing multiple agents including Solver, Verifier, and Corrector, to iteratively refine solutions. While effective in closed-source models like Gemini 2.5 Pro, they struggle to generalize to open-source models due to insufficient critic and correction capabilities. To address this, we propose MarsRL, a novel reinforcement learning framework with agentic pipeline parallelism, designed to jointly optimize all agents in the system. MarsRL introduces agent-specific reward mechanisms to mitigate reward noise and employs pipeline-inspired training to enhance efficiency in handling long trajectories. Applied to Qwen3-30B-A3B-Thinking-2507, MarsRL improves AIME2025 accuracy from 86.5% to 93.3% and BeyondAIME from 64.9% to 73.8%, even surpassing Qwen3-235B-A22B-Thinking-2507. These findings highlight the potential of MarsRL to advance multi-agent reasoning systems and broaden their applicability across diverse reasoning tasks.

We tackle the problem of aligning pre-trained large language models (LMs) with human preferences. If we view text generation as a sequential decision-making problem, reinforcement learning (RL) appears to be a natural conceptual framework. However, using RL for LM-based generation faces empirical challenges, including training instability due to the combinatorial action space, as well as a lack of open-source libraries and benchmarks customized for LM alignment. Thus, a question rises in the research community: is RL a practical paradigm for NLP? To help answer this, we first introduce an open-source modular library, RL4LMs (Reinforcement Learning for Language Models), for optimizing language generators with RL. The library consists of on-policy RL algorithms that can be used to train any encoder or encoder-decoder LM in the HuggingFace library (Wolf et al. 2020) with an arbitrary reward function. Next, we present the GRUE (General Reinforced-language Understanding Evaluation) benchmark, a set of 6 language generation tasks which are supervised not by target strings, but by reward functions which capture automated measures of human preference.GRUE is the first leaderboard-style evaluation of RL algorithms for NLP tasks. Finally, we introduce an easy-to-use, performant RL algorithm, NLPO (Natural Language Policy Optimization)} that learns to effectively reduce the combinatorial action space in language generation. We show 1) that RL techniques are generally better than supervised methods at aligning LMs to human preferences; and 2) that NLPO exhibits greater stability and performance than previous policy gradient methods (e.g., PPO (Schulman et al. 2017)), based on both automatic and human evaluations.

A central paradox in fine-tuning Large Language Models (LLMs) with Reinforcement Learning with Verifiable Reward (RLVR) is the frequent degradation of multi-attempt performance (Pass@k) despite improvements in single-attempt accuracy (Pass@1). This is often accompanied by catastrophic forgetting, where models lose previously acquired skills. While various methods have been proposed, the choice and function of the divergence term have been surprisingly unexamined as a proactive solution. We argue that standard RLVR objectives -- both those using the mode-seeking reverse KL-divergence and those forgoing a divergence term entirely -- lack a crucial mechanism for knowledge retention. The reverse-KL actively accelerates this decay by narrowing the policy, while its absence provides no safeguard against the model drifting from its diverse knowledge base. We propose a fundamental shift in perspective: using the divergence term itself as the solution. Our framework, Diversity-Preserving Hybrid RL (DPH-RL), leverages mass-covering f-divergences (like forward-KL and JS-divergence) to function as a rehearsal mechanism. By continuously referencing the initial policy, this approach forces the model to maintain broad solution coverage. Extensive experiments on math and SQL generation demonstrate that DPH-RL not only resolves the Pass@k degradation but improves both Pass@1 and Pass@k in- and out-of-domain. Additionally, DPH-RL is more training-efficient because it computes f-divergence using generator functions, requiring only sampling from the initial policy and no online reference model. Our work highlights a crucial, overlooked axis for improving RLVR, demonstrating that the proper selection of a divergence measure is a powerful tool for building more general and diverse reasoning models.

Large language models (LLMs) are becoming the foundation for autonomous agents that can use tools to solve complex tasks. Reinforcement learning (RL) has emerged as a common approach for injecting such agentic capabilities, but typically under tightly controlled training setups. It often depends on carefully constructed task-solution pairs and substantial human supervision, which creates a fundamental obstacle to open-ended self-evolution toward superintelligent systems. In this paper, we propose Tool-R0 framework for training general purpose tool-calling agents from scratch with self-play RL, under a zero-data assumption. Initialized from the same base LLM, Tool-R0 co-evolves a Generator and a Solver with complementary rewards: one proposes targeted challenging tasks at the other's competence frontier and the other learns to solve them with real-world tool calls. This creates a self-evolving cycle that requires no pre-existing tasks or datasets. Evaluation on different tool-use benchmarks show that Tool-R0 yields 92.5 relative improvement over the base model and surpasses fully supervised tool-calling baselines under the same setting. Our work further provides empirical insights into self-play LLM agents by analyzing co-evolution, curriculum dynamics, and scaling behavior.

Reward models are essential for aligning Large Language Models (LLMs) with human values, yet their development is hampered by costly preference datasets and poor interpretability. While recent rubric-based approaches offer transparency, they often lack systematic quality control and optimization, creating a trade-off between scalability and reliability. We address these limitations with a novel, training-free framework built on a key assumption: evaluation rubrics underlying human preferences exhibit significant generalization ability across diverse queries, a property that enables remarkable data efficiency. Our two-stage approach first infers high-quality, query-specific rubrics using a validation-guided Propose-Evaluate-Revise pipeline. Second, it generalizes these granular rubrics into a compact, non-redundant core set by maximizing an information-theoretic coding rate. The final output is an interpretable, hierarchical "Theme-Tips" rubric set. Extensive experiments demonstrate the framework's exceptional data efficiency and performance. Critically, using just 70 preference pairs (1.5\% of the source data), our method also empowers smaller models like Qwen3-8B to outperform specialized, fully-trained counterparts. This work pioneers a scalable, interpretable, and data-efficient path for reward modeling.

RSL-RL is an open-source Reinforcement Learning library tailored to the specific needs of the robotics community. Unlike broad general-purpose frameworks, its design philosophy prioritizes a compact and easily modifiable codebase, allowing researchers to adapt and extend algorithms with minimal overhead. The library focuses on algorithms most widely adopted in robotics, together with auxiliary techniques that address robotics-specific challenges. Optimized for GPU-only training, RSL-RL achieves high-throughput performance in large-scale simulation environments. Its effectiveness has been validated in both simulation benchmarks and in real-world robotic experiments, demonstrating its utility as a lightweight, extensible, and practical framework to develop learning-based robotic controllers. The library is open-sourced at: https://github.com/leggedrobotics/rsl_rl.

Reinforcement Learning with Verifiable Rewards (RLVR) has demonstrated success in enhancing LLM reasoning capabilities, but remains limited to single-turn interactions without tool integration. While recent Agentic Reinforcement Learning with Tool use (ARLT) approaches have emerged to address multi-turn tool interactions, existing works develop task-specific codebases that suffer from fragmentation, synchronous execution bottlenecks, and limited extensibility across domains. These inefficiencies hinder broader community adoption and algorithmic innovation. We introduce VerlTool, a unified and modular framework that addresses these limitations through systematic design principles. VerlTool provides four key contributions: (1) upstream alignment with VeRL ensuring compatibility and simplified maintenance, (2) unified tool management via standardized APIs supporting diverse modalities including code execution, search, SQL databases, and vision processing, (3) asynchronous rollout execution achieving near 2times speedup by eliminating synchronization bottlenecks, and (4) comprehensive evaluation demonstrating competitive performance across 6 ARLT domains. Our framework formalizes ARLT as multi-turn trajectories with multi-modal observation tokens (text/image/video), extending beyond single-turn RLVR paradigms. We train and evaluate models on mathematical reasoning, knowledge QA, SQL generation, visual reasoning, web search, and software engineering tasks, achieving results comparable to specialized systems while providing unified training infrastructure. The modular plugin architecture enables rapid tool integration requiring only lightweight Python definitions, significantly reducing development overhead and providing a scalable foundation for tool-augmented RL research. Our code is open-sourced at https://github.com/TIGER-AI-Lab/verl-tool.

Reinforcement learning with verifiable rewards (RLVR) has proven effective in eliciting complex reasoning in large language models (LLMs). However, standard RLVR training often leads to excessively verbose processes (in reasoning tasks) and inefficient exploration trajectories (in agentic settings), as outcome-only rewards provide no incentive for efficiency and the high variance in response length within relatively small rollout groups results in noisy optimization signals. To address this, we propose Rollout Response Recomposition (RoRecomp), a plug-and-play method that guides models toward concise reasoning by strategically recomposing the training data. RoRecomp separates responses into two distinct batch types: 1) priority batches, which combine short-correct and long-incorrect responses selected from online batches to provide a clear gradient signal for brevity, and 2) compensation batches, which utilize remaining responses from a replay buffer to maintain stability and prevent model collapse. To comprehensively evaluate effectiveness, we test RoRecomp across three settings where results demonstrate substantial efficiency gains: reducing reasoning length by 27.7% in zero RL training, reducing unnecessary tool calls by 46.8% while improving accuracy in agentic RL, and achieving up to 52.5% length reduction in thinking compression, all with minimal performance impact.

Reinforcement learning (RL) has demonstrated strong potential in training large language models (LLMs) capable of complex reasoning for real-world problem solving. More recently, RL has been leveraged to create sophisticated LLM-based search agents that adeptly combine reasoning with search engine use. While the use of RL for training search agents is promising, the optimal design of such agents remains not fully understood. In particular, key factors -- such as (1) reward formulation, (2) the choice and characteristics of the underlying LLM, and (3) the role of the search engine in the RL process -- require further investigation. In this work, we conduct comprehensive empirical studies to systematically investigate these and offer actionable insights. We highlight several key findings: format rewards are effective in improving final performance, whereas intermediate retrieval rewards have limited impact; the scale and initialization of the LLM (general-purpose vs. reasoning-specialized) significantly influence RL outcomes; and the choice of search engine plays a critical role in shaping RL training dynamics and the robustness of the trained agent during inference. These establish important guidelines for successfully building and deploying LLM-based search agents in real-world applications. Code is available at https://github.com/PeterGriffinJin/Search-R1.

Reinforcement Learning (RL) is an important machine learning paradigm for solving sequential decision-making problems. Recent years have witnessed remarkable progress in this field due to the rapid development of deep neural networks. However, the success of RL currently relies on extensive training data and computational resources. In addition, RL's limited ability to generalize across tasks restricts its applicability in dynamic and real-world environments. With the arisen of Continual Learning (CL), Continual Reinforcement Learning (CRL) has emerged as a promising research direction to address these limitations by enabling agents to learn continuously, adapt to new tasks, and retain previously acquired knowledge. In this survey, we provide a comprehensive examination of CRL, focusing on its core concepts, challenges, and methodologies. Firstly, we conduct a detailed review of existing works, organizing and analyzing their metrics, tasks, benchmarks, and scenario settings. Secondly, we propose a new taxonomy of CRL methods, categorizing them into four types from the perspective of knowledge storage and/or transfer. Finally, our analysis highlights the unique challenges of CRL and provides practical insights into future directions.

High-quality kernel is critical for scalable AI systems, and enabling LLMs to generate such code would advance AI development. However, training LLMs for this task requires sufficient data, a robust environment, and the process is often vulnerable to reward hacking and lazy optimization. In these cases, models may hack training rewards and prioritize trivial correctness over meaningful speedup. In this paper, we systematically study reinforcement learning (RL) for kernel generation. We first design KernelGYM, a robust distributed GPU environment that supports reward hacking check, data collection from multi-turn interactions and long-term RL training. Building on KernelGYM, we investigate effective multi-turn RL methods and identify a biased policy gradient issue caused by self-inclusion in GRPO. To solve this, we propose Turn-level Reinforce-Leave-One-Out (TRLOO) to provide unbiased advantage estimation for multi-turn RL. To alleviate lazy optimization, we incorporate mismatch correction for training stability and introduce Profiling-based Rewards (PR) and Profiling-based Rejection Sampling (PRS) to overcome the issue. The trained model, Dr.Kernel-14B, reaches performance competitive with Claude-4.5-Sonnet in Kernelbench. Finally, we study sequential test-time scaling for Dr.Kernel-14B. On the KernelBench Level-2 subset, 31.6% of the generated kernels achieve at least a 1.2x speedup over the Torch reference, surpassing Claude-4.5-Sonnet (26.7%) and GPT-5 (28.6%). When selecting the best candidate across all turns, this 1.2x speedup rate further increases to 47.8%. All resources, including environment, training code, models, and dataset, are included in https://www.github.com/hkust-nlp/KernelGYM.

Recently, scaling reinforcement learning with verifiable rewards (RLVR) for large language models (LLMs) has emerged as an effective training paradigm for significantly improving model capabilities, which requires guiding the model to perform extensive exploration and learning, leading to substantial computational overhead and becoming a key challenge. To reduce the number of training steps, Prior work performs linear extrapolation of model parameters. However, the dynamics of model parameter updates during RLVR training remain insufficiently understood. To further investigate the evolution of LLMs during RLVR training, we conduct empirical experiments and find that the rank-1 subspace of the model does not evolve linearly, and its dominance over the original parameters is further amplified during LoRA training. Based on the above insights, we propose the Nonlinear Extrapolation of low-rank trajectories (NExt), a novel framework that models and extrapolates low-rank parameter trajectories in a nonlinear manner. Concretely, we first train the model using LoRA and extract the rank-1 subspace of parameter differences at multiple training steps, which is then used for the subsequent nonlinear extrapolation. Afterward, we utilized the extracted rank-1 subspace to train a predictor, which can model the trajectory of parameter updates during RLVR, and then perform the predict-extend process to extrapolate model parameters, achieving the acceleration of RLVR. To further study and understand NExt, we conduct comprehensive experiments that demonstrate the effectiveness and robustness of the method. Our method reduces computational overhead by approximately 37.5\% while remaining compatible with a wide range of RLVR algorithms and tasks. We release our code in https://github.com/RUCAIBox/NExt.

Large language models (LLMs) excel at reasoning, yet post-training remains critical for aligning their behavior with task goals. Existing reinforcement learning (RL) methods often depend on costly human annotations or external reward models. We propose Reinforcement Learning via Self-Confidence (RLSC), which uses the model's own confidence as reward signals-eliminating the need for labels, preference models, or reward engineering. Applied to Qwen2.5-Math-7B with only 16 samples per question and 10 or 20 training steps, RLSC improves accuracy by +13.4% on AIME2024, +21.2% on MATH500, +21.7% on Minerva Math, +20.8% on Olympiadbench, and +9.7% on AMC23. RLSC provides a simple, scalable post-training method for inference models, requiring only a small number of samples and unlabelled supervision.

Reinforcement Learning with Verifiable Rewards (RLVR) has advanced the reasoning capability of large language models (LLMs), enabling autonomous agents that can conduct effective multi-turn and tool-integrated reasoning. While instructions serve as the primary protocol for defining agents, RLVR typically relies on static and manually designed instructions. However, those instructions may be suboptimal for the base model, and the optimal instruction may change as the agent's policy improves and explores the interaction with the environment. To bridge the gap, we introduce INSPO, a novel Instruction-Policy co-evolution framework that integrates instruction optimization as a dynamic component of the reinforcement learning (RL) loop. INSPO maintains a dynamic population of instruction candidates that are sampled with questions, where reward signals in RL loops are automatically attributed to each instruction, and low performers are periodically pruned. New instructions are generated and verified through an on-policy reflection mechanism, where an LLM-based optimizer analyzes past experience from a replay buffer and evolves more effective strategies given the current policy. We conduct extensive experiments on multi-turn retrieval and reasoning tasks, demonstrating that INSPO substantially outperforms strong baselines relying on static instructions. INSPO discovers innovative instructions that guide the agent toward more strategic reasoning paths, achieving substantial performance gains with only a marginal increase in computational overhead.

Reinforcement learning (RL) has emerged as a pivotal technique for fine-tuning large language models (LLMs) on specific tasks. However, prevailing RL fine-tuning methods predominantly rely on PPO and its variants. Though these algorithms are effective in general RL settings, they often exhibit suboptimal performance and vulnerability to distribution collapse when applied to the fine-tuning of LLMs. In this paper, we propose CORY, extending the RL fine-tuning of LLMs to a sequential cooperative multi-agent reinforcement learning framework, to leverage the inherent coevolution and emergent capabilities of multi-agent systems. In CORY, the LLM to be fine-tuned is initially duplicated into two autonomous agents: a pioneer and an observer. The pioneer generates responses based on queries, while the observer generates responses using both the queries and the pioneer's responses. The two agents are trained together. During training, the agents exchange roles periodically, fostering cooperation and coevolution between them. Experiments evaluate CORY's performance by fine-tuning GPT-2 and Llama-2 under subjective and objective reward functions on the IMDB Review and GSM8K datasets, respectively. Results show that CORY outperforms PPO in terms of policy optimality, resistance to distribution collapse, and training robustness, thereby underscoring its potential as a superior methodology for refining LLMs in real-world applications.

Reinforcement learning (RL) has recently shown strong potential in improving the reasoning capabilities of large language models and is now being actively extended to vision-language models (VLMs). However, existing RL applications in VLMs often rely on heavily engineered frameworks that hinder reproducibility and accessibility, while lacking standardized evaluation protocols, making it difficult to compare results or interpret training dynamics. This work introduces a transparent, from-scratch framework for RL in VLMs, offering a minimal yet functional four-step pipeline validated across multiple models and datasets. In addition, a standardized evaluation scheme is proposed to assess training dynamics and reflective behaviors. Extensive experiments on visual reasoning tasks uncover key empirical findings: response length is sensitive to random seeds, reflection correlates with output length, and RL consistently outperforms supervised fine-tuning (SFT) in generalization, even with high-quality data. These findings, together with the proposed framework, aim to establish a reproducible baseline and support broader engagement in RL-based VLM research.

Vision-Language Models (VLMs) have achieved remarkable progress, yet their large scale often renders them impractical for resource-constrained environments. This paper introduces Unified Reinforcement and Imitation Learning (RIL), a novel and efficient training algorithm designed to create powerful, lightweight VLMs. RIL distinctively combines the strengths of reinforcement learning with adversarial imitation learning. This enables smaller student VLMs not only to mimic the sophisticated text generation of large teacher models but also to systematically improve their generative capabilities through reinforcement signals. Key to our imitation framework is an LLM-based discriminator that adeptly distinguishes between student and teacher outputs, complemented by guidance from multiple large teacher VLMs to ensure diverse learning. This unified learning strategy, leveraging both reinforcement and imitation, empowers student models to achieve significant performance gains, making them competitive with leading closed-source VLMs. Extensive experiments on diverse vision-language benchmarks demonstrate that RIL significantly narrows the performance gap with state-of-the-art open- and closed-source VLMs and, in several instances, surpasses them.

Reinforcement learning (RL) has emerged as a promising approach to improve large language model (LLM) reasoning, yet most open efforts focus narrowly on math and code, limiting our understanding of its broader applicability to general reasoning. A key challenge lies in the lack of reliable, scalable RL reward signals across diverse reasoning domains. We introduce Guru, a curated RL reasoning corpus of 92K verifiable examples spanning six reasoning domains--Math, Code, Science, Logic, Simulation, and Tabular--each built through domain-specific reward design, deduplication, and filtering to ensure reliability and effectiveness for RL training. Based on Guru, we systematically revisit established findings in RL for LLM reasoning and observe significant variation across domains. For example, while prior work suggests that RL primarily elicits existing knowledge from pretrained models, our results reveal a more nuanced pattern: domains frequently seen during pretraining (Math, Code, Science) easily benefit from cross-domain RL training, while domains with limited pretraining exposure (Logic, Simulation, and Tabular) require in-domain training to achieve meaningful performance gains, suggesting that RL is likely to facilitate genuine skill acquisition. Finally, we present Guru-7B and Guru-32B, two models that achieve state-of-the-art performance among open models RL-trained with publicly available data, outperforming best baselines by 7.9% and 6.7% on our 17-task evaluation suite across six reasoning domains. We also show that our models effectively improve the Pass@k performance of their base models, particularly on complex tasks less likely to appear in pretraining data. We release data, models, training and evaluation code to facilitate general-purpose reasoning at: https://github.com/LLM360/Reasoning360

Reward modeling is essential for aligning large language models (LLMs) with human preferences, especially through reinforcement learning from human feedback (RLHF). To provide accurate reward signals, a reward model (RM) should stimulate deep thinking and conduct interpretable reasoning before assigning a score or a judgment. However, existing RMs either produce opaque scalar scores or directly generate the prediction of a preferred answer, making them struggle to integrate natural language critiques, thus lacking interpretability. Inspired by recent advances of long chain-of-thought (CoT) on reasoning-intensive tasks, we hypothesize and validate that integrating reasoning capabilities into reward modeling significantly enhances RM's interpretability and performance. In this work, we introduce a new class of generative reward models -- Reasoning Reward Models (ReasRMs) -- which formulate reward modeling as a reasoning task. We propose a reasoning-oriented training pipeline and train a family of ReasRMs, RM-R1. The training consists of two key stages: (1) distillation of high-quality reasoning chains and (2) reinforcement learning with verifiable rewards. RM-R1 improves LLM rollouts by self-generating reasoning traces or chat-specific rubrics and evaluating candidate responses against them. Empirically, our models achieve state-of-the-art or near state-of-the-art performance of generative RMs across multiple comprehensive reward model benchmarks, outperforming much larger open-weight models (e.g., Llama3.1-405B) and proprietary ones (e.g., GPT-4o) by up to 13.8%. Beyond final performance, we perform thorough empirical analysis to understand the key ingredients of successful ReasRM training. To facilitate future research, we release six ReasRM models along with code and data at https://github.com/RM-R1-UIUC/RM-R1.

Recent progress in vision and language foundation models has significantly advanced multimodal understanding, reasoning, and generation, inspiring a surge of interest in extending such capabilities to embodied settings through vision-language-action (VLA) models. Yet, most VLA models are still trained with supervised fine-tuning (SFT), which struggles to generalize under distribution shifts due to error accumulation. Reinforcement learning (RL) offers a promising alternative by directly optimizing task performance through interaction, but existing attempts remain fragmented and lack a unified platform for fair and systematic comparison across model architectures and algorithmic designs. To address this gap, we introduce RLinf-VLA, a unified and efficient framework for scalable RL training of VLA models. The system adopts a highly flexible resource allocation design that addresses the challenge of integrating rendering, training, and inference in RL+VLA training. In particular, for GPU-parallelized simulators, RLinf-VLA implements a novel hybrid fine-grained pipeline allocation mode, achieving a 1.61x-1.88x speedup in training. Through a unified interface, RLinf-VLA seamlessly supports diverse VLA architectures (e.g., OpenVLA, OpenVLA-OFT), multiple RL algorithms (e.g., PPO, GRPO), and various simulators (e.g., ManiSkill, LIBERO). In simulation, a unified model achieves 98.11\% across 130 LIBERO tasks and 97.66\% across 25 ManiSkill tasks. Beyond empirical performance, our study distills a set of best practices for applying RL to VLA training and sheds light on emerging patterns in this integration. Furthermore, we present preliminary deployment on a real-world Franka robot, where RL-trained policies exhibit stronger generalization than those trained with SFT. We envision RLinf-VLA as a foundation to accelerate and standardize research on embodied intelligence.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key approach for enhancing LLM reasoning.However, standard frameworks like Group Relative Policy Optimization (GRPO) typically employ a uniform rollout budget, leading to resource inefficiency. Moreover, existing adaptive methods often rely on instance-level metrics, such as task pass rates, failing to capture the model's dynamic learning state. To address these limitations, we propose CoBA-RL, a reinforcement learning algorithm designed to adaptively allocate rollout budgets based on the model's evolving capability. Specifically, CoBA-RL utilizes a Capability-Oriented Value function to map tasks to their potential training gains and employs a heap-based greedy strategy to efficiently self-calibrate the distribution of computational resources to samples with high training value. Extensive experiments demonstrate that our approach effectively orchestrates the trade-off between exploration and exploitation, delivering consistent generalization improvements across multiple challenging benchmarks. These findings underscore that quantifying sample training value and optimizing budget allocation are pivotal for advancing LLM post-training efficiency.

Large Language Models (LLMs) are increasingly being explored for building Agents capable of active environmental interaction (e.g., via tool use) to solve complex problems. Reinforcement Learning (RL) is considered a key technology with significant potential for training such Agents; however, the effective application of RL to LLM Agents is still in its nascent stages and faces considerable challenges. Currently, this emerging field lacks in-depth exploration into RL approaches specifically tailored for the LLM Agent context, alongside a scarcity of flexible and easily extensible training frameworks designed for this purpose. To help advance this area, this paper first revisits and clarifies Reinforcement Learning methodologies for LLM Agents by systematically extending the Markov Decision Process (MDP) framework to comprehensively define the key components of an LLM Agent. Secondly, we introduce Agent-R1, a modular, flexible, and user-friendly training framework for RL-based LLM Agents, designed for straightforward adaptation across diverse task scenarios and interactive environments. We conducted experiments on Multihop QA benchmark tasks, providing initial validation for the effectiveness of our proposed methods and framework.

Reinforcement learning (RL) has significantly improved the reasoning ability of large language models. However, current reward models underperform in challenging reasoning scenarios and predominant RL training paradigms rely on rule-based or reference-based rewards, which impose two critical limitations: 1) the dependence on finely annotated reference answer to attain rewards; and 2) the requirement for constrained output format. These limitations fundamentally hinder further RL data scaling and sustained enhancement of model reasoning performance. To address these limitations, we propose a comprehensive framework for evaluating and improving the performance of reward models in complex reasoning scenarios. We first present a reasoning-oriented benchmark (Libra Bench), systematically constructed from a diverse collection of challenging mathematical problems and advanced reasoning models, to address the limitations of existing reward model benchmarks in reasoning scenarios. We further introduce a novel approach for improving the generative reward model via learning-to-think methodologies. Based on the proposed approach, we develop Libra-RM series, a collection of generative reward models with reasoning capabilities that achieve state-of-the-art results on various benchmarks. Comprehensive downstream experiments are conducted and the experimental results demonstrate the correlation between our Libra Bench and downstream application, and the potential of Libra-RM to further improve reasoning models with unlabeled data.

Policy gradient algorithms have been successfully applied to enhance the reasoning capabilities of large language models (LLMs). Despite the widespread use of Kullback-Leibler (KL) regularization in policy gradient algorithms to stabilize training, the systematic exploration of how different KL divergence formulations can be estimated and integrated into surrogate loss functions for online reinforcement learning (RL) presents a nuanced and systematically explorable design space. In this paper, we propose regularized policy gradient (RPG), a systematic framework for deriving and analyzing KL-regularized policy gradient methods in the online RL setting. We derive policy gradients and corresponding surrogate loss functions for objectives regularized by both forward and reverse KL divergences, considering both normalized and unnormalized policy distributions. Furthermore, we present derivations for fully differentiable loss functions as well as REINFORCE-style gradient estimators, accommodating diverse algorithmic needs. We conduct extensive experiments on RL for LLM reasoning using these methods, showing improved or competitive results in terms of training stability and performance compared to strong baselines such as GRPO, REINFORCE++, and DAPO. The code is available at https://github.com/complex-reasoning/RPG.

Reinforcement learning with verifiable rewards (RLVR) has shown great potential to enhance the reasoning ability of large language models (LLMs). However, due to the limited amount of information provided during the RLVR process, the model can only engage in largely blind exploration, which often results in failure on challenging problems. To provide additional information for the RLVR process without relying on a teacher model, we propose A^2D, an Adaptive Ability Decomposing method for enhancing the effectiveness of RLVR. Specifically, we first train a decomposer via RLVR without distillation, enabling it to decompose complex questions into a set of simpler sub-questions. Next, we use this decomposer to annotate sub-questions for each question in the training dataset, and then train the reasoner under RLVR with sub-question guidance. To better understand A^2D, we first compare its performance with competitive baselines, showing its effectiveness. Next, we observe that our method functions as a plug-and-play module that can be applied to different RLVR algorithms. Furthermore, we conduct an analysis of the decomposer, revealing how the RLVR process affects its performance and behavior, and which type of guidance is better suited for enhancing the reasoner's exploration and exploitation abilities.

Training large language models (LLMs) as interactive agents presents unique challenges including long-horizon decision making and interacting with stochastic environment feedback. While reinforcement learning (RL) has enabled progress in static tasks, multi-turn agent RL training remains underexplored. We propose StarPO (State-Thinking-Actions-Reward Policy Optimization), a general framework for trajectory-level agent RL, and introduce RAGEN, a modular system for training and evaluating LLM agents. Our study on three stylized environments reveals three core findings. First, our agent RL training shows a recurring mode of Echo Trap where reward variance cliffs and gradient spikes; we address this with StarPO-S, a stabilized variant with trajectory filtering, critic incorporation, and decoupled clipping. Second, we find the shaping of RL rollouts would benefit from diverse initial states, medium interaction granularity and more frequent sampling. Third, we show that without fine-grained, reasoning-aware reward signals, agent reasoning hardly emerge through multi-turn RL and they may show shallow strategies or hallucinated thoughts. Code and environments are available at https://github.com/RAGEN-AI/RAGEN.

Retrieval-augmented generation (RAG) enables large language models (LLMs) to produce evidence-based responses, and its performance hinges on the matching between the retriever and LLMs. Retriever optimization has emerged as an efficient alternative to fine-tuning LLMs. However, existing solutions suffer from objective mismatch between retriever optimization and the goal of RAG pipeline. Reinforcement learning (RL) provides a promising solution to address this limitation, yet applying RL to retriever optimization introduces two fundamental challenges: 1) the deterministic retrieval is incompatible with RL formulations, and 2) state aliasing arises from query-only retrieval in multi-hop reasoning. To address these challenges, we replace deterministic retrieval with stochastic sampling and formulate RAG as a Markov decision process, making retriever optimizable by RL. Further, we incorporate retrieval history into the state at each retrieval step to mitigate state aliasing. Extensive experiments across diverse RAG pipelines, datasets, and retriever scales demonstrate consistent improvements of our approach in RAG performance.

Reinforcement learning (RL) provides a theoretical framework for continuously improving an agent's behavior via trial and error. However, efficiently learning policies from scratch can be very difficult, particularly for tasks with exploration challenges. In such settings, it might be desirable to initialize RL with an existing policy, offline data, or demonstrations. However, naively performing such initialization in RL often works poorly, especially for value-based methods. In this paper, we present a meta algorithm that can use offline data, demonstrations, or a pre-existing policy to initialize an RL policy, and is compatible with any RL approach. In particular, we propose Jump-Start Reinforcement Learning (JSRL), an algorithm that employs two policies to solve tasks: a guide-policy, and an exploration-policy. By using the guide-policy to form a curriculum of starting states for the exploration-policy, we are able to efficiently improve performance on a set of simulated robotic tasks. We show via experiments that JSRL is able to significantly outperform existing imitation and reinforcement learning algorithms, particularly in the small-data regime. In addition, we provide an upper bound on the sample complexity of JSRL and show that with the help of a guide-policy, one can improve the sample complexity for non-optimism exploration methods from exponential in horizon to polynomial.

Reinforcement learning (RL) has improved guided image generation with diffusion models by directly optimizing rewards that capture image quality, aesthetics, and instruction following capabilities. However, the resulting generative policies inherit the same iterative sampling process of diffusion models that causes slow generation. To overcome this limitation, consistency models proposed learning a new class of generative models that directly map noise to data, resulting in a model that can generate an image in as few as one sampling iteration. In this work, to optimize text-to-image generative models for task specific rewards and enable fast training and inference, we propose a framework for fine-tuning consistency models via RL. Our framework, called Reinforcement Learning for Consistency Model (RLCM), frames the iterative inference process of a consistency model as an RL procedure. RLCM improves upon RL fine-tuned diffusion models on text-to-image generation capabilities and trades computation during inference time for sample quality. Experimentally, we show that RLCM can adapt text-to-image consistency models to objectives that are challenging to express with prompting, such as image compressibility, and those derived from human feedback, such as aesthetic quality. Comparing to RL finetuned diffusion models, RLCM trains significantly faster, improves the quality of the generation measured under the reward objectives, and speeds up the inference procedure by generating high quality images with as few as two inference steps. Our code is available at https://rlcm.owenoertell.com

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a powerful paradigm for facilitating the self-improvement of large language models (LLMs), particularly in the domain of complex reasoning tasks. However, prevailing on-policy RL methods often contend with significant training instability and inefficiency. This is primarily due to a capacity-difficulty mismatch, where the complexity of training data frequently outpaces the model's current capabilities, leading to critically sparse reward signals and stalled learning progress. This challenge is particularly acute for smaller, more resource-efficient LLMs. To overcome this, we introduce the Guided Hybrid Policy Optimization (GHPO), a novel difficulty-aware reinforcement learning framework. GHPO dynamically calibrates task difficulty by employing adaptive prompt refinement to provide targeted guidance. This unique approach adaptively balances direct imitation learning for problems currently beyond the model's reach with exploration-based reinforcement learning for more manageable tasks, effectively creating a smooth and optimized learning curriculum. Extensive experiments demonstrate that GHPO achieves an average performance gain of approximately 5% across six challenging mathematics benchmarks, consistently outperforming strong on-policy reinforcement learning and curriculum learning baselines. Further analysis confirms that our framework significantly enhances both training stability and final reasoning performance, thus offering a scalable and efficient solution for developing powerful and robust reasoning models.

Reinforcement learning (RL) has become a standard paradigm for refining large language models (LLMs) beyond pre-training and instruction tuning. A prominent line of work is RL with verifiable rewards (RLVR), which leverages automatically verifiable outcomes (e.g., correctness or executability) to generate reward signals. While efficient, this framework faces two key limitations: First, its binary feedback is too sparse to capture the quality of the reasoning process. Second, its coarse-grained rewards potentially lead to vanishing gradients. Inspired by observations from human learning, we introduce a RL technique that integrates verifiable outcomes with the model's own confidence estimates. This joint design enriches the reward signal, providing finer-grained feedback and implicitly supervising the reasoning process. Experimental results demonstrate that our proposed method enhances RL performance across multiple datasets and reduces token consumption during inference, while incurring negligible additional training cost. Moreover, it can be used as a plug-in module to enhance other state-of-the-art RL methods.

This paper introduces ARCLE, an environment designed to facilitate reinforcement learning research on the Abstraction and Reasoning Corpus (ARC). Addressing this inductive reasoning benchmark with reinforcement learning presents these challenges: a vast action space, a hard-to-reach goal, and a variety of tasks. We demonstrate that an agent with proximal policy optimization can learn individual tasks through ARCLE. The adoption of non-factorial policies and auxiliary losses led to performance enhancements, effectively mitigating issues associated with action spaces and goal attainment. Based on these insights, we propose several research directions and motivations for using ARCLE, including MAML, GFlowNets, and World Models.

Prevalent reinforcement learning~(RL) methods for fine-tuning LLM reasoners, such as GRPO or Leave-one-out PPO, abandon the learned value function in favor of empirically estimated returns. This hinders test-time compute scaling that relies on using the value-function for verification. In this work, we propose RL^V that augments any ``value-free'' RL method by jointly training the LLM as both a reasoner and a generative verifier using RL-generated data, adding verification capabilities without significant overhead. Empirically, RL^V boosts MATH accuracy by over 20\% with parallel sampling and enables 8-32times efficient test-time compute scaling compared to the base RL method. RL^V also exhibits strong generalization capabilities for both easy-to-hard and out-of-domain tasks. Furthermore, RL^V achieves 1.2-1.6times higher performance when jointly scaling parallel and sequential test-time compute with a long reasoning R1 model.

Recent advances in learning decision-making policies can largely be attributed to training expressive policy models, largely via imitation learning. While imitation learning discards non-expert data, reinforcement learning (RL) can still learn from suboptimal data. However, instantiating RL training of a new policy class often presents a different challenge: most deep RL machinery is co-developed with assumptions on the policy class and backbone, resulting in poor performance when the policy class changes. For instance, SAC utilizes a low-variance reparameterization policy gradient for Gaussian policies, but this is unstable for diffusion policies and intractable for autoregressive categorical policies. To address this issue, we develop an offline RL and online fine-tuning approach called policy-agnostic RL (PA-RL) that can effectively train multiple policy classes, with varying architectures and sizes. We build off the basic idea that a universal supervised learning loss can replace the policy improvement step in RL, as long as it is applied on "optimized" actions. To obtain these optimized actions, we first sample multiple actions from a base policy, and run global optimization (i.e., re-ranking multiple action samples using the Q-function) and local optimization (i.e., running gradient steps on an action sample) to maximize the critic on these candidates. PA-RL enables fine-tuning diffusion and transformer policies with either autoregressive tokens or continuous action outputs, at different sizes, entirely via actor-critic RL. Moreover, PA-RL improves the performance and sample-efficiency by up to 2 times compared to existing offline RL and online fine-tuning methods. We show the first result that successfully fine-tunes OpenVLA, a 7B generalist robot policy, autonomously with Cal-QL, an online RL fine-tuning algorithm, improving from 40% to 70% in the real world in 40 minutes.

Progress in many task domains emerges from repeated revisions to previous solution attempts. Training agents that can reliably self-improve over such sequences at inference-time is a natural target for reinforcement learning (RL), yet the naive approach assumes a fixed maximum iteration depth, which can be both costly and arbitrary. We present Exploratory Iteration (ExIt), a family of autocurriculum RL methods that directly exploits the recurrent structure of self-improvement tasks to train LLMs to perform multi-step self-improvement at inference-time while only training on the most informative single-step iterations. ExIt grows a task space by selectively sampling the most informative intermediate, partial histories encountered during an episode for continued iteration, treating these starting points as new self-iteration task instances to train a self-improvement policy. ExIt can further pair with explicit exploration mechanisms to sustain greater task diversity. Across several domains, encompassing competition math, multi-turn tool-use, and machine learning engineering, we demonstrate that ExIt strategies, starting from either a single or many task instances, can produce policies exhibiting strong inference-time self-improvement on held-out task instances, and the ability to iterate towards higher performance over a step budget extending beyond the average iteration depth encountered during training.

Recent advances in Reinforcement Learning with Verified Reward (RLVR) have driven the emergence of more sophisticated cognitive behaviors in large language models (LLMs), thereby enhancing their reasoning capabilities. However, in prior RLVR pipelines, the repeated use of static initial-state sampling drawn exactly from the dataset distribution during each sampling phase produced overly deterministic, low diversity model behavior, which manifested as rapid entropy collapse and hindered sustained performance gains during prolonged training. To address this issue, we introduce CURE (Critical-token-gUided Re concatenation for Entropy-collapse prevention), a two-stage framework that balances exploration and exploitation. Specifically, in the first stage, to deliberately steer the model toward novel yet coherent contexts, we re-generate at high-entropy critical tokens and jointly optimize the original and the branched trajectories. The further comparison with vanilla DAPO shows that the regeneration process achieves a better performance on math reasoning tasks while sustaining a high-level entropy degree for exploration. In the second stage, we continue training with static initial-state sampling by DAPO, intentionally placing the model in a familiar state to gradually strengthen exploitation. Extensive experiments on Qwen-2.5-Math-7B show that, compared to other RLVR methods, CURE achieves a 5% performance gain across six math benchmarks, establishing state-of-the-art performance in both entropy and accuracy. A series of experiments further validate the effectiveness of our approach. Code is available at https://github.com/bytedance/CURE.

Reinforcement Learning with Verifiable Rewards (RLVR) has catalyzed significant breakthroughs in complex LLM reasoning within verifiable domains, such as mathematics and programming. Recent efforts have sought to extend this paradigm to open-ended tasks by employing LLMs-as-a-Judge to provide sequence-level rewards for policy optimization. However, these rewards are inherently sparse, failing to provide the fine-grained supervision necessary for generating complex, long-form trajectories. Furthermore, current work treats the Judge as a black-box oracle, discarding the rich intermediate feedback signals encoded in it. To address these limitations, we introduce Grad2Reward, a novel framework that extracts dense process rewards directly from the Judge's model inference process via a single backward pass. By leveraging gradient-based attribution, Grad2Reward enables precise token-level credit assignment, substantially enhancing training efficiency and reasoning quality. Additionally, Grad2Reward introduces a self-judging mechanism, allowing the policy to improve through its own evaluative signals without training specialized reward models or reliance on superior external Judges. The experiments demonstrate that policies optimized with Grad2Reward achieve outstanding performance across diverse open-ended tasks, affirming its effectiveness and broad generalizability.

Reward models play a critical role in guiding large language models toward outputs that align with human expectations. However, an open challenge remains in effectively utilizing test-time compute to enhance reward model performance. In this work, we introduce Reward Reasoning Models (RRMs), which are specifically designed to execute a deliberate reasoning process before generating final rewards. Through chain-of-thought reasoning, RRMs leverage additional test-time compute for complex queries where appropriate rewards are not immediately apparent. To develop RRMs, we implement a reinforcement learning framework that fosters self-evolved reward reasoning capabilities without requiring explicit reasoning traces as training data. Experimental results demonstrate that RRMs achieve superior performance on reward modeling benchmarks across diverse domains. Notably, we show that RRMs can adaptively exploit test-time compute to further improve reward accuracy. The pretrained reward reasoning models are available at https://huggingface.co/Reward-Reasoning.

Denoising-based generative models, particularly diffusion and flow matching algorithms, have achieved remarkable success. However, aligning their output distributions with complex downstream objectives, such as human preferences, compositional accuracy, or data compressibility, remains challenging. While reinforcement learning (RL) fine-tuning methods, inspired by advances in RL from human feedback (RLHF) for large language models, have been adapted to these generative frameworks, current RL approaches are suboptimal for diffusion models and offer limited flexibility in controlling alignment strength after fine-tuning. In this work, we reinterpret RL fine-tuning for diffusion models through the lens of stochastic differential equations and implicit reward conditioning. We introduce Reinforcement Learning Guidance (RLG), an inference-time method that adapts Classifier-Free Guidance (CFG) by combining the outputs of the base and RL fine-tuned models via a geometric average. Our theoretical analysis shows that RLG's guidance scale is mathematically equivalent to adjusting the KL-regularization coefficient in standard RL objectives, enabling dynamic control over the alignment-quality trade-off without further training. Extensive experiments demonstrate that RLG consistently improves the performance of RL fine-tuned models across various architectures, RL algorithms, and downstream tasks, including human preferences, compositional control, compressibility, and text rendering. Furthermore, RLG supports both interpolation and extrapolation, thereby offering unprecedented flexibility in controlling generative alignment. Our approach provides a practical and theoretically sound solution for enhancing and controlling diffusion model alignment at inference. The source code for RLG is publicly available at the Github: https://github.com/jinluo12345/Reinforcement-learning-guidance.

The growing disparity between the exponential scaling of computational resources and the finite growth of high-quality text data now constrains conventional scaling approaches for large language models (LLMs). To address this challenge, we introduce Reinforcement Learning on Pre-Training data (RLPT), a new training-time scaling paradigm for optimizing LLMs. In contrast to prior approaches that scale training primarily through supervised learning, RLPT enables the policy to autonomously explore meaningful trajectories to learn from pre-training data and improve its capability through reinforcement learning (RL). While existing RL strategies such as reinforcement learning from human feedback (RLHF) and reinforcement learning with verifiable rewards (RLVR) rely on human annotation for reward construction, RLPT eliminates this dependency by deriving reward signals directly from pre-training data. Specifically, it adopts a next-segment reasoning objective, rewarding the policy for accurately predicting subsequent text segments conditioned on the preceding context. This formulation allows RL to be scaled on pre-training data, encouraging the exploration of richer trajectories across broader contexts and thereby fostering more generalizable reasoning skills. Extensive experiments on both general-domain and mathematical reasoning benchmarks across multiple models validate the effectiveness of RLPT. For example, when applied to Qwen3-4B-Base, RLPT yields absolute improvements of 3.0, 5.1, 8.1, 6.0, 6.6, and 5.3 on MMLU, MMLU-Pro, GPQA-Diamond, KOR-Bench, AIME24, and AIME25, respectively. The results further demonstrate favorable scaling behavior, suggesting strong potential for continued gains with more compute. In addition, RLPT provides a solid foundation, extending the reasoning boundaries of LLMs and enhancing RLVR performance.

Preference-based Reinforcement Learning (PbRL) is a paradigm in which an RL agent learns to optimize a task using pair-wise preference-based feedback over trajectories, rather than explicit reward signals. While PbRL has demonstrated practical success in fine-tuning language models, existing theoretical work focuses on regret minimization and fails to capture most of the practical frameworks. In this study, we fill in such a gap between theoretical PbRL and practical algorithms by proposing a theoretical reward-agnostic PbRL framework where exploratory trajectories that enable accurate learning of hidden reward functions are acquired before collecting any human feedback. Theoretical analysis demonstrates that our algorithm requires less human feedback for learning the optimal policy under preference-based models with linear parameterization and unknown transitions, compared to the existing theoretical literature. Specifically, our framework can incorporate linear and low-rank MDPs with efficient sample complexity. Additionally, we investigate reward-agnostic RL with action-based comparison feedback and introduce an efficient querying algorithm tailored to this scenario.

Generative information retrieval (GenIR) is a promising neural retrieval paradigm that formulates document retrieval as a document identifier (docid) generation task, allowing for end-to-end optimization toward a unified global retrieval objective. However, existing GenIR models suffer from token-level misalignment, where models trained to predict the next token often fail to capture document-level relevance effectively. While reinforcement learning-based methods, such as reinforcement learning from relevance feedback (RLRF), aim to address this misalignment through reward modeling, they introduce significant complexity, requiring the optimization of an auxiliary reward function followed by reinforcement fine-tuning, which is computationally expensive and often unstable. To address these challenges, we propose direct document relevance optimization (DDRO), which aligns token-level docid generation with document-level relevance estimation through direct optimization via pairwise ranking, eliminating the need for explicit reward modeling and reinforcement learning. Experimental results on benchmark datasets, including MS MARCO document and Natural Questions, show that DDRO outperforms reinforcement learning-based methods, achieving a 7.4% improvement in MRR@10 for MS MARCO and a 19.9% improvement for Natural Questions. These findings highlight DDRO's potential to enhance retrieval effectiveness with a simplified optimization approach. By framing alignment as a direct optimization problem, DDRO simplifies the ranking optimization pipeline of GenIR models while offering a viable alternative to reinforcement learning-based methods.

Reinforcement Learning with Verifiable Rewards (RLVR) is a promising paradigm for enhancing the reasoning ability in Large Language Models (LLMs). However, prevailing methods primarily rely on self-exploration or a single off-policy teacher to elicit long chain-of-thought (LongCoT) reasoning, which may introduce intrinsic model biases and restrict exploration, ultimately limiting reasoning diversity and performance. Drawing inspiration from multi-teacher strategies in knowledge distillation, we introduce Adaptive Multi-Guidance Policy Optimization (AMPO), a novel framework that adaptively leverages guidance from multiple proficient teacher models, but only when the on-policy model fails to generate correct solutions. This "guidance-on-demand" approach expands exploration while preserving the value of self-discovery. Moreover, AMPO incorporates a comprehension-based selection mechanism, prompting the student to learn from the reasoning paths that it is most likely to comprehend, thus balancing broad exploration with effective exploitation. Extensive experiments show AMPO substantially outperforms a strong baseline (GRPO), with a 4.3% improvement on mathematical reasoning tasks and 12.2% on out-of-distribution tasks, while significantly boosting Pass@k performance and enabling more diverse exploration. Notably, using four peer-sized teachers, our method achieves comparable results to approaches that leverage a single, more powerful teacher (e.g., DeepSeek-R1) with more data. These results demonstrate a more efficient and scalable path to superior reasoning and generalizability. Our code is available at https://github.com/SII-Enigma/AMPO.

In this paper, we survey recent advances in Reinforcement Learning (RL) for reasoning with Large Language Models (LLMs). RL has achieved remarkable success in advancing the frontier of LLM capabilities, particularly in addressing complex logical tasks such as mathematics and coding. As a result, RL has emerged as a foundational methodology for transforming LLMs into LRMs. With the rapid progress of the field, further scaling of RL for LRMs now faces foundational challenges not only in computational resources but also in algorithm design, training data, and infrastructure. To this end, it is timely to revisit the development of this domain, reassess its trajectory, and explore strategies to enhance the scalability of RL toward Artificial SuperIntelligence (ASI). In particular, we examine research applying RL to LLMs and LRMs for reasoning abilities, especially since the release of DeepSeek-R1, including foundational components, core problems, training resources, and downstream applications, to identify future opportunities and directions for this rapidly evolving area. We hope this review will promote future research on RL for broader reasoning models. Github: https://github.com/TsinghuaC3I/Awesome-RL-for-LRMs

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising approach for training reasoning language models (RLMs) by leveraging supervision from verifiers. Although verifier implementation is easier than solution annotation for many tasks, existing synthetic data generation methods remain largely solution-centric, while verifier-based methods rely on a few hand-crafted procedural environments. In this work, we scale RLVR by introducing ReSyn, a pipeline that generates diverse reasoning environments equipped with instance generators and verifiers, covering tasks such as constraint satisfaction, algorithmic puzzles, and spatial reasoning. A Qwen2.5-7B-Instruct model trained with RL on ReSyn data achieves consistent gains across reasoning benchmarks and out-of-domain math benchmarks, including a 27\% relative improvement on the challenging BBEH benchmark. Ablations show that verifier-based supervision and increased task diversity both contribute significantly, providing empirical evidence that generating reasoning environments at scale can enhance reasoning abilities in RLMs

Large language models for mathematical reasoning are typically trained with outcome-based rewards, which credit only the final answer. In our experiments, we observe that this paradigm is highly susceptible to reward hacking, leading to a substantial overestimation of a model's reasoning ability. This is evidenced by a high incidence of false positives - solutions that reach the correct final answer through an unsound reasoning process. Through a systematic analysis with human verification, we establish a taxonomy of these failure modes, identifying patterns like Miracle Steps - abrupt jumps to a correct output without a valid preceding derivation. Probing experiments suggest a strong association between these Miracle Steps and memorization, where the model appears to recall the answer directly rather than deriving it. To mitigate this systemic issue, we introduce the Rubric Reward Model (RRM), a process-oriented reward function that evaluates the entire reasoning trajectory against problem-specific rubrics. The generative RRM provides fine-grained, calibrated rewards (0-1) that explicitly penalize logical flaws and encourage rigorous deduction. When integrated into a reinforcement learning pipeline, RRM-based training consistently outperforms outcome-only supervision across four math benchmarks. Notably, it boosts Verified Pass@1024 on AIME2024 from 26.7% to 62.6% and reduces the incidence of Miracle Steps by 71%. Our work demonstrates that rewarding the solution process is crucial for building models that are not only more accurate but also more reliable.

Large-scale reinforcement learning with verifiable rewards (RLVR) has demonstrated its effectiveness in harnessing the potential of large language models (LLMs) for single-turn reasoning tasks. In realistic reasoning scenarios, LLMs can often utilize external tools to assist in task-solving processes. However, current RL algorithms inadequately balance the models' intrinsic long-horizon reasoning capabilities and their proficiency in multi-turn tool interactions. To bridge this gap, we propose Agentic Reinforced Policy Optimization (ARPO), a novel agentic RL algorithm tailored for training multi-turn LLM-based agents. Through preliminary experiments, we observe that LLMs tend to exhibit highly uncertain behavior, characterized by an increase in the entropy distribution of generated tokens, immediately following interactions with external tools. Motivated by this observation, ARPO incorporates an entropy-based adaptive rollout mechanism, dynamically balancing global trajectory sampling and step-level sampling, thereby promoting exploration at steps with high uncertainty after tool usage. By integrating an advantage attribution estimation, ARPO enables LLMs to internalize advantage differences in stepwise tool-use interactions. Our experiments across 13 challenging benchmarks in computational reasoning, knowledge reasoning, and deep search domains demonstrate ARPO's superiority over trajectory-level RL algorithms. Remarkably, ARPO achieves improved performance using only half of the tool-use budget required by existing methods, offering a scalable solution for aligning LLM-based agents with real-time dynamic environments. Our code and datasets are released at https://github.com/dongguanting/ARPO

Reinforcement learning with verifiable rewards (RLVR) has recently enhanced the reasoning capabilities of large language models (LLMs), particularly for mathematical problem solving. However, a fundamental limitation remains: as the sampling budget increases, the advantage of RLVR-trained models over their pretrained bases often diminishes or even vanishes, revealing a strong dependence on the base model's restricted search space. We attribute this phenomenon to the widespread use of the reverse Kullback-Leibler (KL) divergence regularizer, whose mode-seeking behavior keeps the policy trapped inside the base model's support region and hampers wider exploration. To address this issue, we propose RAPO (Rewards-Aware Policy Optimization), an algorithm to promote broader yet focused exploration. Our method (i) utilizes the forward KL penalty to replace the reverse KL penalty for out-of-distribution exploration, and (ii) reweights the reference policy to facilitate adaptive in-distribution exploration. We train Qwen2.5-3B and 7B models with RAPO on the 8K SimpleRL-Zero dataset, without supervised fine-tuning, and evaluate them on AIME2024 and AIME2025. Results show that RAPO consistently improves problem-solving performance. Notably, RAPO enables models to surpass the base model's performance ceiling and solves previously intractable problems, advancing the frontier of RLVR for challenging reasoning tasks.

As web platforms evolve towards greater personalization and emotional complexity, conversational agents must transcend superficial empathy to demonstrate identity-aware emotional reasoning. However, existing systems face two limitations: (1) reliance on situation-centric datasets lacking persistent user identity, which hampers the capture of personalized affective nuances; and (2) dependence on opaque, coarse reward signals that hinder development of verifiable empathetic reasoning. To address these gaps, we introduce KardiaBench, a large-scale user-grounded benchmark comprising 178,080 QA pairs across 22,080 multi-turn conversations anchored to 671 real-world profiles. The dataset is constructed via a model-in-the-loop pipeline with iterative rubric-guided refinement to ensure psychological plausibility and persona consistency. This progressive empathy pipeline that integrates user comprehension, contextual reasoning, and emotion perception into conversations, followed by iterative critique and rubric-based refinement to ensure psychological plausibility, emotional fidelity, and persona consistency. Building on this, we propose Kardia-R1, a framework that trains models for interpretable, stepwise empathetic cognition. Kardia-R1 leverages Rubric-as-Judge Empathetic Reinforcement Learning (Rubric-ERL), a GRPO-based method that uses explainable, human-aligned rubric rewards to tightly couple user understanding, emotional inference, and supportive response generation. Extensive experiments across four LLM backbones demonstrate that Kardia-R1 consistently outperforms othet methods in emotion accuracy, empathy, relevance, persona consistency, and safety. Our dataset and model will be released at https://github.com/JhCircle/Kardia-R1.

Reinforcement learning (RL) is typically concerned with estimating stationary policies or single-step models, leveraging the Markov property to factorize problems in time. However, we can also view RL as a generic sequence modeling problem, with the goal being to produce a sequence of actions that leads to a sequence of high rewards. Viewed in this way, it is tempting to consider whether high-capacity sequence prediction models that work well in other domains, such as natural-language processing, can also provide effective solutions to the RL problem. To this end, we explore how RL can be tackled with the tools of sequence modeling, using a Transformer architecture to model distributions over trajectories and repurposing beam search as a planning algorithm. Framing RL as sequence modeling problem simplifies a range of design decisions, allowing us to dispense with many of the components common in offline RL algorithms. We demonstrate the flexibility of this approach across long-horizon dynamics prediction, imitation learning, goal-conditioned RL, and offline RL. Further, we show that this approach can be combined with existing model-free algorithms to yield a state-of-the-art planner in sparse-reward, long-horizon tasks.