Daily Papers

Large language models (LLMs) have demonstrated exceptional reasoning capabilities, and co-evolving paradigms have shown promising results in domains such as code and math. However, in scientific reasoning tasks, these models remain fragile due to unreliable solution evaluation and limited diversity in verification strategies. In this work, we propose Sci-CoE, a two-stage scientific co-evolving framework that enables models to self-evolve as both solver and verifier through a transition from sparse supervision to unsupervised learning. In the first stage, the model uses a small set of annotated data to establish fundamental correctness judgment anchors for the Verifier. In the second stage, we introduce a geometric reward mechanism that jointly considers consensus, reliability, and diversity, driving large-scale self-iteration on unlabeled data. Experiments on several general scientific benchmarks demonstrate that Sci-CoE enhances complex reasoning capabilities and exhibits strong scalability, facilitating the construction of more robust and diverse evaluation systems. Codes are available at https://github.com/InternScience/Sci-CoE.

Multimodal Large Language Models (MLLMs) struggle with complex geometric reasoning, largely because "black box" outcome-based supervision fails to distinguish between lucky guesses and rigorous deduction. To address this, we introduce a paradigm shift towards subgoal-level evaluation and learning. We first construct GeoGoal, a benchmark synthesized via a rigorous formal verification data engine, which converts abstract proofs into verifiable numeric subgoals. This structure reveals a critical divergence between reasoning quality and outcome accuracy. Leveraging this, we propose the Sub-Goal Verifiable Reward (SGVR) framework, which replaces sparse signals with dense rewards based on the Skeleton Rate. Experiments demonstrate that SGVR not only enhances geometric performance (+9.7%) but also exhibits strong generalization, transferring gains to general math (+8.0%) and other general reasoning tasks (+2.8%), demonstrating broad applicability across diverse domains.

Video diffusion models lack explicit geometric supervision during training, leading to inconsistency artifacts such as object deformation, spatial drift, and depth violations in generated videos. To address this limitation, we propose a geometry-based reward model that leverages pretrained geometric foundation models to evaluate multi-view consistency through cross-frame reprojection error. Unlike previous geometric metrics that measure inconsistency in pixel space, where pixel intensity may introduce additional noise, our approach conducts error computation in a pointwise fashion, yielding a more physically grounded and robust error metric. Furthermore, we introduce a geometry-aware sampling strategy that filters out low-texture and non-semantic regions, focusing evaluation on geometrically meaningful areas with reliable correspondences to improve robustness. We apply this reward model to align video diffusion models through two complementary pathways: post-training of a bidirectional model via SFT or Reinforcement Learning and inference-time optimization of a Causal Video Model (e.g., Streaming video generator) via test-time scaling with our reward as a path verifier. Experimental results validate the effectiveness of our design, demonstrating that our geometry-based reward provides superior robustness compared to other variants. By enabling efficient inference-time scaling, our method offers a practical solution for enhancing open-source video models without requiring extensive computational resources for retraining.

While recent 3D generative models can produce high-quality texture images, they often fail to capture human preferences or meet task-specific requirements. Moreover, a core challenge in the 3D texture generation domain is that most existing approaches rely on repeated calls to 2D text-to-image generative models, which lack an inherent understanding of the 3D structure of the input 3D mesh object. To alleviate these issues, we propose an end-to-end differentiable, reinforcement-learning-free framework that embeds human feedback, expressed as differentiable reward functions, directly into the 3D texture synthesis pipeline. By back-propagating preference signals through both geometric and appearance modules of the proposed framework, our method generates textures that respect the 3D geometry structure and align with desired criteria. To demonstrate its versatility, we introduce three novel geometry-aware reward functions, which offer a more controllable and interpretable pathway for creating high-quality 3D content from natural language. By conducting qualitative, quantitative, and user-preference evaluations against state-of-the-art methods, we demonstrate that our proposed strategy consistently outperforms existing approaches. We will make our implementation code publicly available upon acceptance of the paper.

Implementing a reward function that perfectly captures a complex task in the real world is impractical. As a result, it is often appropriate to think of the reward function as a proxy for the true objective rather than as its definition. We study this phenomenon through the lens of Goodhart's law, which predicts that increasing optimisation of an imperfect proxy beyond some critical point decreases performance on the true objective. First, we propose a way to quantify the magnitude of this effect and show empirically that optimising an imperfect proxy reward often leads to the behaviour predicted by Goodhart's law for a wide range of environments and reward functions. We then provide a geometric explanation for why Goodhart's law occurs in Markov decision processes. We use these theoretical insights to propose an optimal early stopping method that provably avoids the aforementioned pitfall and derive theoretical regret bounds for this method. Moreover, we derive a training method that maximises worst-case reward, for the setting where there is uncertainty about the true reward function. Finally, we evaluate our early stopping method experimentally. Our results support a foundation for a theoretically-principled study of reinforcement learning under reward misspecification.

Designing reward functions for efficiently guiding reinforcement learning (RL) agents toward specific behaviors is a complex task. This is challenging since it requires the identification of reward structures that are not sparse and that avoid inadvertently inducing undesirable behaviors. Naively modifying the reward structure to offer denser and more frequent feedback can lead to unintended outcomes and promote behaviors that are not aligned with the designer's intended goal. Although potential-based reward shaping is often suggested as a remedy, we systematically investigate settings where deploying it often significantly impairs performance. To address these issues, we introduce a new framework that uses a bi-level objective to learn behavior alignment reward functions. These functions integrate auxiliary rewards reflecting a designer's heuristics and domain knowledge with the environment's primary rewards. Our approach automatically determines the most effective way to blend these types of feedback, thereby enhancing robustness against heuristic reward misspecification. Remarkably, it can also adapt an agent's policy optimization process to mitigate suboptimalities resulting from limitations and biases inherent in the underlying RL algorithms. We evaluate our method's efficacy on a diverse set of tasks, from small-scale experiments to high-dimensional control challenges. We investigate heuristic auxiliary rewards of varying quality -- some of which are beneficial and others detrimental to the learning process. Our results show that our framework offers a robust and principled way to integrate designer-specified heuristics. It not only addresses key shortcomings of existing approaches but also consistently leads to high-performing solutions, even when given misaligned or poorly-specified auxiliary reward functions.

Synthetic data is crucial for advancing autonomous driving (AD) systems, yet current state-of-the-art video generation models, despite their visual realism, suffer from subtle geometric distortions that limit their utility for downstream perception tasks. We identify and quantify this critical issue, demonstrating a significant performance gap in 3D object detection when using synthetic versus real data. To address this, we introduce Reinforcement Learning with Geometric Feedback (RLGF), RLGF uniquely refines video diffusion models by incorporating rewards from specialized latent-space AD perception models. Its core components include an efficient Latent-Space Windowing Optimization technique for targeted feedback during diffusion, and a Hierarchical Geometric Reward (HGR) system providing multi-level rewards for point-line-plane alignment, and scene occupancy coherence. To quantify these distortions, we propose GeoScores. Applied to models like DiVE on nuScenes, RLGF substantially reduces geometric errors (e.g., VP error by 21\%, Depth error by 57\%) and dramatically improves 3D object detection mAP by 12.7\%, narrowing the gap to real-data performance. RLGF offers a plug-and-play solution for generating geometrically sound and reliable synthetic videos for AD development.

Reinforcement learning usually uses the feedback rewards of environmental to train agents. But the rewards in the actual environment are sparse, and even some environments will not rewards. Most of the current methods are difficult to get good performance in sparse reward or non-reward environments. Although using shaped rewards is effective when solving sparse reward tasks, it is limited to specific problems and learning is also susceptible to local optima. We propose a model-free method that does not rely on environmental rewards to solve the problem of sparse rewards in the general environment. Our method use the minimum number of transitions between states as the distance to replace the rewards of environmental, and proposes a goal-distance gradient to achieve policy improvement. We also introduce a bridge point planning method based on the characteristics of our method to improve exploration efficiency, thereby solving more complex tasks. Experiments show that our method performs better on sparse reward and local optimal problems in complex environments than previous work.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

A successful tactic that is followed by the scientific community for advancing AI is to treat games as problems, which has been proven to lead to various breakthroughs. We adapt this strategy in order to study Rocket League, a widely popular but rather under-explored 3D multiplayer video game with a distinct physics engine and complex dynamics that pose a significant challenge in developing efficient and high-performance game-playing agents. In this paper, we present Lucy-SKG, a Reinforcement Learning-based model that learned how to play Rocket League in a sample-efficient manner, outperforming by a notable margin the two highest-ranking bots in this game, namely Necto (2022 bot champion) and its successor Nexto, thus becoming a state-of-the-art agent. Our contributions include: a) the development of a reward analysis and visualization library, b) novel parameterizable reward shape functions that capture the utility of complex reward types via our proposed Kinesthetic Reward Combination (KRC) technique, and c) design of auxiliary neural architectures for training on reward prediction and state representation tasks in an on-policy fashion for enhanced efficiency in learning speed and performance. By performing thorough ablation studies for each component of Lucy-SKG, we showed their independent effectiveness in overall performance. In doing so, we demonstrate the prospects and challenges of using sample-efficient Reinforcement Learning techniques for controlling complex dynamical systems under competitive team-based multiplayer conditions.

Reward models are key in reinforcement learning from human feedback (RLHF) systems, aligning the model behavior with human preferences. Particularly in the math domain, there have been plenty of studies using reward models to align policies for improving reasoning capabilities. Recently, as the importance of reward models has been emphasized, RewardBench is proposed to understand their behavior. However, we figure out that the math subset of RewardBench has different representations between chosen and rejected completions, and relies on a single comparison, which may lead to unreliable results as it only see an isolated case. Therefore, it fails to accurately present the robustness of reward models, leading to a misunderstanding of its performance and potentially resulting in reward hacking. In this work, we introduce a new design for reliable evaluation of reward models, and to validate this, we construct RewardMATH, a benchmark that effectively represents the robustness of reward models in mathematical reasoning tasks. We demonstrate that the scores on RewardMATH strongly correlate with the results of optimized policy and effectively estimate reward overoptimization, whereas the existing benchmark shows almost no correlation. The results underscore the potential of our design to enhance the reliability of evaluation, and represent the robustness of reward model. We make our code and data publicly available.

In goal-reaching reinforcement learning (RL), the optimal value function has a particular geometry, called quasimetric structure. This paper introduces Quasimetric Reinforcement Learning (QRL), a new RL method that utilizes quasimetric models to learn optimal value functions. Distinct from prior approaches, the QRL objective is specifically designed for quasimetrics, and provides strong theoretical recovery guarantees. Empirically, we conduct thorough analyses on a discretized MountainCar environment, identifying properties of QRL and its advantages over alternatives. On offline and online goal-reaching benchmarks, QRL also demonstrates improved sample efficiency and performance, across both state-based and image-based observations.

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.

Geometric methods for solving open-world off-road navigation tasks, by learning occupancy and metric maps, provide good generalization but can be brittle in outdoor environments that violate their assumptions (e.g., tall grass). Learning-based methods can directly learn collision-free behavior from raw observations, but are difficult to integrate with standard geometry-based pipelines. This creates an unfortunate conflict -- either use learning and lose out on well-understood geometric navigational components, or do not use it, in favor of extensively hand-tuned geometry-based cost maps. In this work, we reject this dichotomy by designing the learning and non-learning-based components in a way such that they can be effectively combined in a self-supervised manner. Both components contribute to a planning criterion: the learned component contributes predicted traversability as rewards, while the geometric component contributes obstacle cost information. We instantiate and comparatively evaluate our system in both in-distribution and out-of-distribution environments, showing that this approach inherits complementary gains from the learned and geometric components and significantly outperforms either of them. Videos of our results are hosted at https://sites.google.com/view/hybrid-imitative-planning

Weight-perturbation evolution strategies (ES) can fine-tune billion-parameter language models with surprisingly small populations (e.g., N!approx!30), contradicting classical zeroth-order curse-of-dimensionality intuition. We also observe a second seemingly separate phenomenon: under fixed hyperparameters, the stochastic fine-tuning reward often rises, peaks, and then degrades in both ES and GRPO. We argue that both effects reflect a shared geometric property of fine-tuning landscapes: they are low-dimensional in curvature. A small set of high-curvature dimensions dominates improvement, producing (i) heterogeneous time scales that yield rise-then-decay under fixed stochasticity, as captured by a minimal quadratic stochastic-ascent model, and (ii) degenerate improving updates, where many random perturbations share similar components along these directions. Using ES as a geometric probe on fine-tuning reward landscapes of GSM8K, ARC-C, and WinoGrande across Qwen2.5-Instruct models (0.5B--7B), we show that reward-improving perturbations remain empirically accessible with small populations across scales. Together, these results reconcile ES scalability with non-monotonic training dynamics and suggest that high-dimensional fine-tuning may admit a broader class of viable optimization methods than worst-case theory implies.

Large reasoning models (LRMs) have recently shown promise in solving complex math problems when optimized with Reinforcement Learning (RL). But conventional approaches rely on outcome-only rewards that provide sparse feedback, resulting in inefficient optimization process. In this work, we investigate the function of process reward models (PRMs) to accelerate the RL training for LRMs. We propose a novel intrinsic signal-driven generative process evaluation mechanism operating at the thought level to address major bottlenecks in RL-based training. Specifically, instead of requiring PRMs to know how to solve problems, our method uses intrinsic signals in solutions to judge stepwise correctness and aggregate contiguous correct/incorrect steps into coherent 'thought' units. This structured, thought-level rewards enable more reliable credit assignment by reducing ambiguity in step segmentation and alleviating reward hacking. We further introduce a capability-adaptive reward mechanism that dynamically balances exploration and exploitation based on the LRM's current proficiency, guiding learning without stifling creative trial-and-error. These innovations are integrated into a new off-policy RL algorithm, TP-GRPO, which extends grouped proximal optimization with process-based rewards and improves training efficiency. Experiments on 1.5B and 7B parameter LRMs demonstrate that our method achieves higher problem-solving accuracy with significantly fewer training samples than outcome-only reward baselines. The results validate that well-structured process rewards can substantially accelerate LRM optimization in math reasoning tasks. Code is available at https://github.com/cs-holder/tp_grpo.

We introduce Talk2Move, a reinforcement learning (RL) based diffusion framework for text-instructed spatial transformation of objects within scenes. Spatially manipulating objects in a scene through natural language poses a challenge for multimodal generation systems. While existing text-based manipulation methods can adjust appearance or style, they struggle to perform object-level geometric transformations-such as translating, rotating, or resizing objects-due to scarce paired supervision and pixel-level optimization limits. Talk2Move employs Group Relative Policy Optimization (GRPO) to explore geometric actions through diverse rollouts generated from input images and lightweight textual variations, removing the need for costly paired data. A spatial reward guided model aligns geometric transformations with linguistic description, while off-policy step evaluation and active step sampling improve learning efficiency by focusing on informative transformation stages. Furthermore, we design object-centric spatial rewards that evaluate displacement, rotation, and scaling behaviors directly, enabling interpretable and coherent transformations. Experiments on curated benchmarks demonstrate that Talk2Move achieves precise, consistent, and semantically faithful object transformations, outperforming existing text-guided editing approaches in both spatial accuracy and scene coherence.

Large-scale video diffusion models achieve impressive visual quality, yet often fail to preserve geometric consistency. Prior approaches improve consistency either by augmenting the generator with additional modules or applying geometry-aware alignment. However, architectural modifications can compromise the generalization of internet-scale pretrained models, while existing alignment methods are limited to static scenes and rely on RGB-space rewards that require repeated VAE decoding, incurring substantial compute overhead and failing to generalize to highly dynamic real-world scenes. To preserve the pretrained capacity while improving geometric consistency, we propose VGGRPO (Visual Geometry GRPO), a latent geometry-guided framework for geometry-aware video post-training. VGGRPO introduces a Latent Geometry Model (LGM) that stitches video diffusion latents to geometry foundation models, enabling direct decoding of scene geometry from the latent space. By constructing LGM from a geometry model with 4D reconstruction capability, VGGRPO naturally extends to dynamic scenes, overcoming the static-scene limitations of prior methods. Building on this, we perform latent-space Group Relative Policy Optimization with two complementary rewards: a camera motion smoothness reward that penalizes jittery trajectories, and a geometry reprojection consistency reward that enforces cross-view geometric coherence. Experiments on both static and dynamic benchmarks show that VGGRPO improves camera stability, geometry consistency, and overall quality while eliminating costly VAE decoding, making latent-space geometry-guided reinforcement an efficient and flexible approach to world-consistent video generation.

We present AIRS: Automatic Intrinsic Reward Shaping that intelligently and adaptively provides high-quality intrinsic rewards to enhance exploration in reinforcement learning (RL). More specifically, AIRS selects shaping function from a predefined set based on the estimated task return in real-time, providing reliable exploration incentives and alleviating the biased objective problem. Moreover, we develop an intrinsic reward toolkit to provide efficient and reliable implementations of diverse intrinsic reward approaches. We test AIRS on various tasks of MiniGrid, Procgen, and DeepMind Control Suite. Extensive simulation demonstrates that AIRS can outperform the benchmarking schemes and achieve superior performance with simple architecture.

Reward functions are central in reinforcement learning (RL), guiding agents towards optimal decision-making. The complexity of RL tasks requires meticulously designed reward functions that effectively drive learning while avoiding unintended consequences. Effective reward design aims to provide signals that accelerate the agent's convergence to optimal behavior. Crafting rewards that align with task objectives, foster desired behaviors, and prevent undesirable actions is inherently challenging. This thesis delves into the critical role of reward signals in RL, highlighting their impact on the agent's behavior and learning dynamics and addressing challenges such as delayed, ambiguous, or intricate rewards. In this thesis work, we tackle different aspects of reward shaping. First, we address the problem of designing informative and interpretable reward signals from a teacher's/expert's perspective (teacher-driven). Here, the expert, equipped with the optimal policy and the corresponding value function, designs reward signals that expedite the agent's convergence to optimal behavior. Second, we build on this teacher-driven approach by introducing a novel method for adaptive interpretable reward design. In this scenario, the expert tailors the rewards based on the learner's current policy, ensuring alignment and optimal progression. Third, we propose a meta-learning approach, enabling the agent to self-design its reward signals online without expert input (agent-driven). This self-driven method considers the agent's learning and exploration to establish a self-improving feedback loop.

Intrinsic reward shaping has emerged as a prevalent approach to solving hard-exploration and sparse-rewards environments in reinforcement learning (RL). While single intrinsic rewards, such as curiosity-driven or novelty-based methods, have shown effectiveness, they often limit the diversity and efficiency of exploration. Moreover, the potential and principle of combining multiple intrinsic rewards remains insufficiently explored. To address this gap, we introduce HIRE (Hybrid Intrinsic REward), a flexible and elegant framework for creating hybrid intrinsic rewards through deliberate fusion strategies. With HIRE, we conduct a systematic analysis of the application of hybrid intrinsic rewards in both general and unsupervised RL across multiple benchmarks. Extensive experiments demonstrate that HIRE can significantly enhance exploration efficiency and diversity, as well as skill acquisition in complex and dynamic settings.

Multimodal large language models have various practical applications that demand strong reasoning abilities. Despite recent advancements, these models still struggle to solve complex geometric problems. A key challenge stems from the lack of high-quality image-text pair datasets for understanding geometric images. Furthermore, most template-based data synthesis pipelines typically fail to generalize to questions beyond their predefined templates. In this paper, we bridge this gap by introducing a complementary process of Reinforcement Learning with Verifiable Rewards (RLVR) into the data generation pipeline. By adopting RLVR to refine captions for geometric images synthesized from 50 basic geometric relations and using reward signals derived from mathematical problem-solving tasks, our pipeline successfully captures the key features of geometry problem-solving. This enables better task generalization and yields non-trivial improvements. Furthermore, even in out-of-distribution scenarios, the generated dataset enhances the general reasoning capabilities of multimodal large language models, yielding accuracy improvements of 2.8%-4.8% in statistics, arithmetic, algebraic, and numerical tasks with non-geometric input images of MathVista and MathVerse, along with 2.4%-3.9% improvements in Art, Design, Tech, and Engineering tasks in MMMU.

Extrinsic rewards can effectively guide reinforcement learning (RL) agents in specific tasks. However, extrinsic rewards frequently fall short in complex environments due to the significant human effort needed for their design and annotation. This limitation underscores the necessity for intrinsic rewards, which offer auxiliary and dense signals and can enable agents to learn in an unsupervised manner. Although various intrinsic reward formulations have been proposed, their implementation and optimization details are insufficiently explored and lack standardization, thereby hindering research progress. To address this gap, we introduce RLeXplore, a unified, highly modularized, and plug-and-play framework offering reliable implementations of eight state-of-the-art intrinsic reward methods. Furthermore, we conduct an in-depth study that identifies critical implementation details and establishes well-justified standard practices in intrinsically-motivated RL. Our documentation, examples, and source code are available at https://github.com/RLE-Foundation/RLeXplore.

Incorporating a robotic manipulator into a wheel-legged robot enhances its agility and expands its potential for practical applications. However, the presence of potential instability and uncertainties presents additional challenges for control objectives. In this paper, we introduce an arm-constrained curriculum learning architecture to tackle the issues introduced by adding the manipulator. Firstly, we develop an arm-constrained reinforcement learning algorithm to ensure safety and stability in control performance. Additionally, to address discrepancies in reward settings between the arm and the base, we propose a reward-aware curriculum learning method. The policy is first trained in Isaac gym and transferred to the physical robot to do dynamic grasping tasks, including the door-opening task, fan-twitching task and the relay-baton-picking and following task. The results demonstrate that our proposed approach effectively controls the arm-equipped wheel-legged robot to master dynamic grasping skills, allowing it to chase and catch a moving object while in motion. Please refer to our website (https://acodedog.github.io/wheel-legged-loco-manipulation) for the code and supplemental videos.

Reward sparsity in long-horizon reinforcement learning (RL) tasks remains a significant challenge, while existing outcome-based reward shaping struggles to define meaningful immediate rewards without introducing bias or requiring explicit task decomposition. Alternatively, verification-based reward shaping uses stepwise critics, but misalignment between immediate rewards and long-term objectives can lead to reward hacking and suboptimal policies. In this work, we address this problem in the context of software engineering (SWE) tasks, where multi-turn reasoning and rule-based verification are critical. We introduce the SWE-oriented RL Framework, a unified system supporting multi-turn interaction, docker-based execution, and customizable reward functions. Additionally, we propose Gated Reward Accumulation (G-RA), a novel method that accumulates immediate rewards only when high-level (long-term) rewards meet a predefined threshold, ensuring stable RL optimization. Experiments on SWE-bench Verified and kBench demonstrate that G-RA leads to an increase in completion rates (47.6\% \rightarrow 93.8\% and 22.0\% \rightarrow 86.0\%) and modification rates (19.6\% \rightarrow 23.8\% and 12.0\% \rightarrow 42.0\%), while avoiding policy degradation caused by reward misalignment. Our findings highlight the importance of balanced reward accumulation in long-horizon RL and provide a practical solution.

Reward design is a fundamental, yet challenging aspect of practical reinforcement learning (RL). For simple tasks, researchers typically handcraft the reward function, e.g., using a linear combination of several reward factors. However, such reward engineering is subject to approximation bias, incurs large tuning cost, and often cannot provide the granularity required for complex tasks. To avoid these difficulties, researchers have turned to reinforcement learning from human feedback (RLHF), which learns a reward function from human preferences between pairs of trajectory sequences. By leveraging preference-based reward modeling, RLHF learns complex rewards that are well aligned with human preferences, allowing RL to tackle increasingly difficult problems. Unfortunately, the applicability of RLHF is limited due to the high cost and difficulty of obtaining human preference data. In light of this cost, we investigate learning reward functions for complex tasks with less human effort; simply by ranking the importance of the reward factors. More specifically, we propose a new RL framework -- HERON, which compares trajectories using a hierarchical decision tree induced by the given ranking. These comparisons are used to train a preference-based reward model, which is then used for policy learning. We find that our framework can not only train high performing agents on a variety of difficult tasks, but also provide additional benefits such as improved sample efficiency and robustness. Our code is available at https://github.com/abukharin3/HERON.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a crucial paradigm for incentivizing reasoning capabilities in Large Language Models (LLMs). Due to vast state-action spaces and reward sparsity in reasoning tasks, existing methods often struggle with deficient exploration and poor sample efficiency. In the paper, we propose DIVER (Diversity-Incentivized Exploration for VersatilE Reasoning), an innovative framework that highlights the pivotal role of global sequence-level diversity to incentivize deep exploration for versatile reasoning. We first conduct a primary empirical study to reveal a strong positive correlation between global diversity and reasoning capacity. Building on this insight, we introduce global diversity incentives as an intrinsic reward to promote deep exploration in a semantically structured space. Incorporating the intrinsic reward, we develop a potential-based reward shaping mechanism to preserve optimal policy invariance and design simple heuristics to mitigate possible reward hacking. Experimental results show that DIVER outperforms competitive RLVR baselines with various exploration strategies on both in-domain and out-of-domain tasks, excelling in both Pass@1 and Pass@k evaluations. Our code is available at https://github.com/NJU-RL/DIVER.

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.

In order to solve a task using reinforcement learning, it is necessary to first formalise the goal of that task as a reward function. However, for many real-world tasks, it is very difficult to manually specify a reward function that never incentivises undesirable behaviour. As a result, it is increasingly popular to use reward learning algorithms, which attempt to learn a reward function from data. However, the theoretical foundations of reward learning are not yet well-developed. In particular, it is typically not known when a given reward learning algorithm with high probability will learn a reward function that is safe to optimise. This means that reward learning algorithms generally must be evaluated empirically, which is expensive, and that their failure modes are difficult to anticipate in advance. One of the roadblocks to deriving better theoretical guarantees is the lack of good methods for quantifying the difference between reward functions. In this paper we provide a solution to this problem, in the form of a class of pseudometrics on the space of all reward functions that we call STARC (STAndardised Reward Comparison) metrics. We show that STARC metrics induce both an upper and a lower bound on worst-case regret, which implies that our metrics are tight, and that any metric with the same properties must be bilipschitz equivalent to ours. Moreover, we also identify a number of issues with reward metrics proposed by earlier works. Finally, we evaluate our metrics empirically, to demonstrate their practical efficacy. STARC metrics can be used to make both theoretical and empirical analysis of reward learning algorithms both easier and more principled.

Unsupervised reinforcement learning with verifiable rewards (URLVR) offers a pathway to scale LLM training beyond the supervision bottleneck by deriving rewards without ground truth labels. Recent works leverage model intrinsic signals, showing promising early gains, yet their potential and limitations remain unclear. In this work, we revisit URLVR and provide a comprehensive analysis spanning taxonomy, theory and extensive experiments. We first classify URLVR methods into intrinsic versus external based on reward sources, then establish a unified theoretical framework revealing that all intrinsic methods converge toward sharpening the model's initial distribution This sharpening mechanism succeeds when initial confidence aligns with correctness but fails catastrophically when misaligned. Through systematic experiments, we show intrinsic rewards consistently follow a rise-then-fall pattern across methods, with collapse timing determined by model prior rather than engineering choices. Despite these scaling limits, we find intrinsic rewards remain valuable in test-time training on small datasets, and propose Model Collapse Step to measure model prior, serving as a practical indicator for RL trainability. Finally, we explore external reward methods that ground verification in computational asymmetries, showing preliminary evidence they may escape the confidence-correctness ceiling. Our findings chart boundaries for intrinsic URLVR while motivating paths toward scalable alternatives.

Finding meaningful and accurate dense rewards is a fundamental task in the field of reinforcement learning (RL) that enables agents to explore environments more efficiently. In traditional RL settings, agents learn optimal policies through interactions with an environment guided by reward signals. However, when these signals are sparse, delayed, or poorly aligned with the intended task objectives, agents often struggle to learn effectively. Dense reward functions, which provide informative feedback at every step or state transition, offer a potential solution by shaping agent behavior and accelerating learning. Despite their benefits, poorly crafted reward functions can lead to unintended behaviors, reward hacking, or inefficient exploration. This problem is particularly acute in complex or high-dimensional environments where handcrafted rewards are difficult to specify and validate. To address this, recent research has explored a variety of approaches, including inverse reinforcement learning, reward modeling from human preferences, and self-supervised learning of intrinsic rewards. While these methods offer promising directions, they often involve trade-offs between generality, scalability, and alignment with human intent. This proposal explores several approaches to dealing with these unsolved problems and enhancing the effectiveness and reliability of dense reward construction in different RL applications.

The success of Reinforcement Learning from Human Feedback (RLHF) critically depends on the quality of the reward model. While this quality is primarily evaluated through accuracy, it remains unclear whether accuracy fully captures what makes a reward model an effective teacher. We address this question from an optimization perspective. First, we prove that regardless of how accurate a reward model is, if it induces low reward variance, then the RLHF objective suffers from a flat landscape. Consequently, even a perfectly accurate reward model can lead to extremely slow optimization, underperforming less accurate models that induce higher reward variance. We additionally show that a reward model that works well for one language model can induce low reward variance, and thus a flat objective landscape, for another. These results establish a fundamental limitation of evaluating reward models solely based on accuracy or independently of the language model they guide. Experiments using models of up to 8B parameters corroborate our theory, demonstrating the interplay between reward variance, accuracy, and reward maximization rate. Overall, our findings highlight that beyond accuracy, a reward model needs to induce sufficient variance for efficient optimization.

The primary obstacle for applying reinforcement learning (RL) to real-world robotics is the design of effective reward functions. While recently learning-based Process Reward Models (PRMs) are a promising direction, they are often hindered by two fundamental limitations: their reward models lack step-aware understanding and rely on single-view perception, leading to unreliable assessments of fine-grained manipulation progress; and their reward shaping procedures are theoretically unsound, often inducing a semantic trap that misguides policy optimization. To address these, we introduce Dopamine-Reward, a novel reward modeling method for learning a general-purpose, step-aware process reward model from multi-view inputs. At its core is our General Reward Model (GRM), trained on a vast 3,400+ hour dataset, which leverages Step-wise Reward Discretization for structural understanding and Multi-Perspective Reward Fusion to overcome perceptual limitations. Building upon Dopamine-Reward, we propose Dopamine-RL, a robust policy learning framework that employs a theoretically-sound Policy-Invariant Reward Shaping method, which enables the agent to leverage dense rewards for efficient self-improvement without altering the optimal policy, thereby fundamentally avoiding the semantic trap. Extensive experiments across diverse simulated and real-world tasks validate our approach. GRM achieves state-of-the-art accuracy in reward assessment, and Dopamine-RL built on GRM significantly improves policy learning efficiency. For instance, after GRM is adapted to a new task in a one-shot manner from a single expert trajectory, the resulting reward model enables Dopamine-RL to improve the policy from near-zero to 95% success with only 150 online rollouts (approximately 1 hour of real robot interaction), while retaining strong generalization across tasks. Project website: https://robo-dopamine.github.io

Reinforcement learning (RL) agents often face challenges in balancing exploration and exploitation, particularly in environments where sparse or dense rewards bias learning. Biological systems, such as human toddlers, naturally navigate this balance by transitioning from free exploration with sparse rewards to goal-directed behavior guided by increasingly dense rewards. Inspired by this natural progression, we investigate the Toddler-Inspired Reward Transition in goal-oriented RL tasks. Our study focuses on transitioning from sparse to potential-based dense (S2D) rewards while preserving optimal strategies. Through experiments on dynamic robotic arm manipulation and egocentric 3D navigation tasks, we demonstrate that effective S2D reward transitions significantly enhance learning performance and sample efficiency. Additionally, using a Cross-Density Visualizer, we show that S2D transitions smooth the policy loss landscape, resulting in wider minima that improve generalization in RL models. In addition, we reinterpret Tolman's maze experiments, underscoring the critical role of early free exploratory learning in the context of S2D rewards.

Recent progress in text-to-image generation has greatly advanced visual fidelity and creativity, but it has also imposed higher demands on prompt complexity-particularly in encoding intricate spatial relationships. In such cases, achieving satisfactory results often requires multiple sampling attempts. To address this challenge, we introduce a novel method that strengthens the spatial understanding of current image generation models. We first construct the SpatialReward-Dataset with over 80k preference pairs. Building on this dataset, we build SpatialScore, a reward model designed to evaluate the accuracy of spatial relationships in text-to-image generation, achieving performance that even surpasses leading proprietary models on spatial evaluation. We further demonstrate that this reward model effectively enables online reinforcement learning for the complex spatial generation. Extensive experiments across multiple benchmarks show that our specialized reward model yields significant and consistent gains in spatial understanding for image generation.

Can reinforcement learning with hard, verifiable rewards teach a compact language model to reason about physics, or does it primarily learn to pattern-match toward correct answers? We study this question by training a 1.5B-parameter reasoning model on beam statics, a classic engineering problem, using parameter-efficient RLVR with binary correctness rewards from symbolic solvers, without teacher-generated reasoning traces. The best BeamPERL checkpoint achieves a 66.7% improvement in Pass@1 over the base model. However, the learned competence is anisotropic: the model generalizes compositionally (more loads) but fails under topological shifts (moved supports) that require the same equilibrium equations. Intermediate checkpoints yield the strongest reasoning, while continued optimization degrades robustness while maintaining reward. These findings reveal a key limitation of outcome-level alignment: reinforcement learning with exact physics rewards induces procedural solution templates rather than internalization of governing equations. The precision of the reward signal - even when analytically exact - does not by itself guarantee transferable physical reasoning. Our results suggest that verifiable rewards may need to be paired with structured reasoning scaffolding to move beyond template matching toward robust scientific reasoning.

Curiosity-based reward schemes can present powerful exploration mechanisms which facilitate the discovery of solutions for complex, sparse or long-horizon tasks. However, as the agent learns to reach previously unexplored spaces and the objective adapts to reward new areas, many behaviours emerge only to disappear due to being overwritten by the constantly shifting objective. We argue that merely using curiosity for fast environment exploration or as a bonus reward for a specific task does not harness the full potential of this technique and misses useful skills. Instead, we propose to shift the focus towards retaining the behaviours which emerge during curiosity-based learning. We posit that these self-discovered behaviours serve as valuable skills in an agent's repertoire to solve related tasks. Our experiments demonstrate the continuous shift in behaviour throughout training and the benefits of a simple policy snapshot method to reuse discovered behaviour for transfer tasks.

Reward function design and exploration time are arguably the biggest obstacles to the deployment of reinforcement learning (RL) agents in the real world. In many real-world tasks, designing a reward function takes considerable hand engineering and often requires additional sensors to be installed just to measure whether the task has been executed successfully. Furthermore, many interesting tasks consist of multiple implicit intermediate steps that must be executed in sequence. Even when the final outcome can be measured, it does not necessarily provide feedback on these intermediate steps. To address these issues, we propose leveraging the abstraction power of intermediate visual representations learned by deep models to quickly infer perceptual reward functions from small numbers of demonstrations. We present a method that is able to identify key intermediate steps of a task from only a handful of demonstration sequences, and automatically identify the most discriminative features for identifying these steps. This method makes use of the features in a pre-trained deep model, but does not require any explicit specification of sub-goals. The resulting reward functions can then be used by an RL agent to learn to perform the task in real-world settings. To evaluate the learned reward, we present qualitative results on two real-world tasks and a quantitative evaluation against a human-designed reward function. We also show that our method can be used to learn a real-world door opening skill using a real robot, even when the demonstration used for reward learning is provided by a human using their own hand. To our knowledge, these are the first results showing that complex robotic manipulation skills can be learned directly and without supervised labels from a video of a human performing the task. Supplementary material and data are available at https://sermanet.github.io/rewards

One of the challenges in applying reinforcement learning in a complex real-world environment lies in providing the agent with a sufficiently detailed reward function. Any misalignment between the reward and the desired behavior can result in unwanted outcomes. This may lead to issues like "reward hacking" where the agent maximizes rewards by unintended behavior. In this work, we propose to disentangle the reward into two distinct parts. A simple task-specific reward, outlining the particulars of the task at hand, and an unknown common-sense reward, indicating the expected behavior of the agent within the environment. We then explore how this common-sense reward can be learned from expert demonstrations. We first show that inverse reinforcement learning, even when it succeeds in training an agent, does not learn a useful reward function. That is, training a new agent with the learned reward does not impair the desired behaviors. We then demonstrate that this problem can be solved by training simultaneously on multiple tasks. That is, multi-task inverse reinforcement learning can be applied to learn a useful reward function.

In reinforcement learning (RL), an agent learns to perform a task by interacting with an environment and receiving feedback (a numerical reward) for its actions. However, the assumption that rewards are always observable is often not applicable in real-world problems. For example, the agent may need to ask a human to supervise its actions or activate a monitoring system to receive feedback. There may even be a period of time before rewards become observable, or a period of time after which rewards are no longer given. In other words, there are cases where the environment generates rewards in response to the agent's actions but the agent cannot observe them. In this paper, we formalize a novel but general RL framework - Monitored MDPs - where the agent cannot always observe rewards. We discuss the theoretical and practical consequences of this setting, show challenges raised even in toy environments, and propose algorithms to begin to tackle this novel setting. This paper introduces a powerful new formalism that encompasses both new and existing problems and lays the foundation for future research.

We study a class of reinforcement learning problems where the reward signals for policy learning are generated by a discriminator that is dependent on and jointly optimized with the policy. This interdependence between the policy and the discriminator leads to an unstable learning process because reward signals from an immature discriminator are noisy and impede policy learning, and conversely, an untrained policy impedes discriminator learning. We call this learning setting Internally Rewarded Reinforcement Learning (IRRL) as the reward is not provided directly by the environment but internally by the discriminator. In this paper, we formally formulate IRRL and present a class of problems that belong to IRRL. We theoretically derive and empirically analyze the effect of the reward function in IRRL and based on these analyses propose the clipped linear reward function. Experimental results show that the proposed reward function can consistently stabilize the training process by reducing the impact of reward noise, which leads to faster convergence and higher performance compared with baselines in diverse tasks.

In this work, we introduce CAD-Coder, a novel framework that reformulates text-to-CAD as the generation of CadQuery scripts - a Python-based, parametric CAD language. This representation enables direct geometric validation, a richer modeling vocabulary, and seamless integration with existing LLMs. To further enhance code validity and geometric fidelity, we propose a two-stage learning pipeline: (1) supervised fine-tuning on paired text-CadQuery data, and (2) reinforcement learning with Group Reward Policy Optimization (GRPO), guided by a CAD-specific reward comprising both a geometric reward (Chamfer Distance) and a format reward. We also introduce a chain-of-thought (CoT) planning process to improve model reasoning, and construct a large-scale, high-quality dataset of 110K text-CadQuery-3D model triplets and 1.5K CoT samples via an automated pipeline. Extensive experiments demonstrate that CAD-Coder enables LLMs to generate diverse, valid, and complex CAD models directly from natural language, advancing the state of the art of text-to-CAD generation and geometric reasoning.

Recent advancements adopt online reinforcement learning (RL) from LLMs to text-to-image rectified flow diffusion models for reward alignment. The use of group-level rewards successfully aligns the model with the targeted reward. However, it faces challenges including low efficiency, dependency on stochastic samplers, and reward hacking. The problem is that rectified flow models are fundamentally different from LLMs: 1) For efficiency, online image sampling takes much more time and dominates the time of training. 2) For stochasticity, rectified flow is deterministic once the initial noise is fixed. Aiming at these problems and inspired by the effects of group-level rewards from LLMs, we design Group-level Direct Reward Optimization (GDRO). GDRO is a new post-training paradigm for group-level reward alignment that combines the characteristics of rectified flow models. Through rigorous theoretical analysis, we point out that GDRO supports full offline training that saves the large time cost for image rollout sampling. Also, it is diffusion-sampler-independent, which eliminates the need for the ODE-to-SDE approximation to obtain stochasticity. We also empirically study the reward hacking trap that may mislead the evaluation, and involve this factor in the evaluation using a corrected score that not only considers the original evaluation reward but also the trend of reward hacking. Extensive experiments demonstrate that GDRO effectively and efficiently improves the reward score of the diffusion model through group-wise offline optimization across the OCR and GenEval tasks, while demonstrating strong stability and robustness in mitigating reward hacking.

Many reinforcement learning environments (e.g., Minecraft) provide only sparse rewards that indicate task completion or failure with binary values. The challenge in exploration efficiency in such environments makes it difficult for reinforcement-learning-based agents to learn complex tasks. To address this, this paper introduces an advanced learning system, named Auto MC-Reward, that leverages Large Language Models (LLMs) to automatically design dense reward functions, thereby enhancing the learning efficiency. Auto MC-Reward consists of three important components: Reward Designer, Reward Critic, and Trajectory Analyzer. Given the environment information and task descriptions, the Reward Designer first design the reward function by coding an executable Python function with predefined observation inputs. Then, our Reward Critic will be responsible for verifying the code, checking whether the code is self-consistent and free of syntax and semantic errors. Further, the Trajectory Analyzer summarizes possible failure causes and provides refinement suggestions according to collected trajectories. In the next round, Reward Designer will further refine and iterate the dense reward function based on feedback. Experiments demonstrate a significant improvement in the success rate and learning efficiency of our agents in complex tasks in Minecraft, such as obtaining diamond with the efficient ability to avoid lava, and efficiently explore trees and animals that are sparse in the plains biome.

Although reinforcement learning with verifiable rewards (RLVR) shows promise in improving the reasoning ability of large language models (LLMs), the scaling up dilemma remains due to the reliance on human annotated labels especially for complex tasks. Recent alternatives that explore various self-reward signals exhibit the eliciting potential of LLM reasoning, but suffer from the non-negligible collapse issue. Inspired by the success of self-supervised learning, we propose Co-Reward, a novel RL framework that leverages contrastive agreement across semantically analogical questions as a reward basis. Specifically, we construct a similar question for each training sample (without labels) and synthesize their individual surrogate labels through a simple rollout voting, and then the reward is constructed by cross-referring the labels of each question pair to enforce the internal reasoning consistency across analogical inputs. Intuitively, such a self-supervised reward-shaping mechanism increases the difficulty of learning collapse into a trivial solution, and promotes stable reasoning elicitation and improvement through expanding the input sample variants. Empirically, Co-Reward achieves superior performance compared to other self-reward baselines on multiple reasoning benchmarks and LLM series, and reaches or even surpasses ground-truth (GT) labeled reward, with improvements of up to +6.8% on MATH500 over GT reward on Llama-3.2-3B-Instruct. Our code is publicly available at https://github.com/tmlr-group/Co-Reward.

Large Language Models (LLMs) have excelled as high-level semantic planners for sequential decision-making tasks. However, harnessing them to learn complex low-level manipulation tasks, such as dexterous pen spinning, remains an open problem. We bridge this fundamental gap and present Eureka, a human-level reward design algorithm powered by LLMs. Eureka exploits the remarkable zero-shot generation, code-writing, and in-context improvement capabilities of state-of-the-art LLMs, such as GPT-4, to perform evolutionary optimization over reward code. The resulting rewards can then be used to acquire complex skills via reinforcement learning. Without any task-specific prompting or pre-defined reward templates, Eureka generates reward functions that outperform expert human-engineered rewards. In a diverse suite of 29 open-source RL environments that include 10 distinct robot morphologies, Eureka outperforms human experts on 83% of the tasks, leading to an average normalized improvement of 52%. The generality of Eureka also enables a new gradient-free in-context learning approach to reinforcement learning from human feedback (RLHF), readily incorporating human inputs to improve the quality and the safety of the generated rewards without model updating. Finally, using Eureka rewards in a curriculum learning setting, we demonstrate for the first time, a simulated Shadow Hand capable of performing pen spinning tricks, adeptly manipulating a pen in circles at rapid speed.

Reinforcement Learning (RL) has shown great potential in refining robotic manipulation policies, yet its efficacy remains strongly bottlenecked by the difficulty of designing generalizable reward functions. In this paper, we propose a framework for online policy refinement by adapting foundation VLMs into online reward generators. We develop a robust, scalable reward model based on a state-of-the-art VLM, trained on a large-scale, multi-source dataset encompassing real-world robot trajectories, human-object interactions, and diverse simulated environments. Unlike prior approaches that evaluate entire trajectories post-hoc, our method leverages the VLM to formulate a multifaceted reward signal comprising process, completion, and temporal contrastive rewards based on current visual observations. Initializing with a base policy trained via Imitation Learning (IL), we employ these VLM rewards to guide the model to correct sub-optimal behaviors in a closed-loop manner. We evaluate our framework on challenging long-horizon manipulation benchmarks requiring sequential execution and precise control. Crucially, our reward model operates in a purely zero-shot manner within these test environments. Experimental results demonstrate that our method significantly improves the success rate of the initial IL policy within just 30 RL iterations, demonstrating remarkable sample efficiency. This empirical evidence highlights that VLM-generated signals can provide reliable feedback to resolve execution errors, effectively eliminating the need for manual reward engineering and facilitating efficient online refinement for robot learning.

We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

Reinforcement learning with verifiable rewards has emerged as a powerful paradigm for training intelligent agents. However, existing methods typically employ binary rewards that fail to capture quality differences among trajectories achieving identical outcomes, thereby overlooking potential diversity within the solution space. Inspired by the ``sweet spot'' concept in tennis-the racket's core region that produces optimal hitting effects, we introduce Sweet Spot Learning (SSL), a novel framework that provides differentiated guidance for agent optimization. SSL follows a simple yet effective principle: progressively amplified, tiered rewards guide policies toward the sweet-spot region of the solution space. This principle naturally adapts across diverse tasks: visual perception tasks leverage distance-tiered modeling to reward proximity, while complex reasoning tasks reward incremental progress toward promising solutions. We theoretically demonstrate that SSL preserves optimal solution ordering and enhances the gradient signal-to-noise ratio, thereby fostering more directed optimization. Extensive experiments across GUI perception, short/long-term planning, and complex reasoning tasks show consistent improvements over strong baselines on 12 benchmarks, achieving up to 2.5X sample efficiency gains and effective cross-task transferability. Our work establishes SSL as a general principle for training capable and robust agents.

Reinforcement Learning from Human Feedback (RLHF) is essential for aligning large language models (LLMs) with human values. However, RLHF is susceptible to reward hacking, where the agent exploits flaws in the reward function rather than learning the intended behavior, thus degrading alignment. While reward shaping helps stabilize RLHF and partially mitigate reward hacking, a systematic investigation into shaping techniques and their underlying principles remains lacking. To bridge this gap, we present a comprehensive study of the prevalent reward shaping methods. Our analysis suggests three key design principles: (1) RL reward is ideally bounded, (2) RL benefits from rapid initial growth followed by gradual convergence, and (3) RL reward is best formulated as a function of centered reward. Guided by these insights, we propose Preference As Reward (PAR), a novel approach that leverages the latent preferences embedded within the reward model itself as the signal for reinforcement learning. We evaluated PAR on two base models, Gemma2-2B and Llama3-8B, using two datasets, Ultrafeedback-Binarized and HH-RLHF. Experimental results demonstrate PAR's superior performance over other reward shaping methods. On the AlpacaEval 2.0 benchmark, PAR achieves a win rate at least 5 percentage points higher than competing approaches. Furthermore, PAR exhibits remarkable data efficiency, requiring only a single reference reward for optimal performance, and maintains robustness against reward hacking even after two full epochs of training. Code is available at https://github.com/PorUna-byte/PAR.

Large-scale robot learning has recently shown promise for enabling robots to perform complex tasks by integrating perception, control, and language understanding. Yet, it struggles with long-horizon, contact-rich manipulation such as deformable object handling, where demonstration quality is inconsistent. Reward modeling offers a natural solution: by providing grounded progress signals, it transforms noisy demonstrations into stable supervision that generalizes across diverse trajectories. We introduce a stage-aware, video-based reward modeling framework that jointly predicts high-level task stages and fine-grained progress. Reward labels are automatically derived from natural language subtask annotations, ensuring consistent progress estimation across variable-length demonstrations. This design overcomes frame-index labeling, which fails in variable-duration tasks like folding a T-shirt. Our reward model demonstrates robustness to variability, generalization to out-of-distribution settings, and strong utility for policy training. Building on it, we propose Reward-Aligned Behavior Cloning (RA-BC), which filters high-quality data and reweights samples by reward. Experiments show the reward model alone outperforms baselines on validation and real robot rollouts. Integrated into RA-BC, our approach achieves 83% success on folding T-shirts from the flattened state and 67% from the crumpled state -- far surpassing vanilla behavior cloning, which attains only 8% and 0% success. Overall, our results highlight reward modeling as a key enabler for scalable, annotation-efficient, and robust imitation learning in long-horizon manipulation.

In classical Reinforcement Learning from Human Feedback (RLHF), Reward Models (RMs) serve as the fundamental signal provider for model alignment. As Large Language Models evolve into agentic systems capable of autonomous tool invocation and complex reasoning, the paradigm of reward modeling faces unprecedented challenges--most notably, the lack of benchmarks specifically designed to assess RM capabilities within tool-integrated environments. To address this gap, we present Plan-RewardBench, a trajectory-level preference benchmark designed to evaluate how well judges distinguish preferred versus distractor agent trajectories in complex tool-using scenarios. Plan-RewardBench covers four representative task families -- (i) Safety Refusal, (ii) Tool-Irrelevance / Unavailability, (iii) Complex Planning, and (iv) Robust Error Recovery -- comprising validated positive trajectories and confusable hard negatives constructed via multi-model natural rollouts, rule-based perturbations, and minimal-edit LLM perturbations. We benchmark representative RMs (generative, discriminative, and LLM-as-Judge) under a unified pairwise protocol, reporting accuracy trends across varying trajectory lengths and task categories. Furthermore, we provide diagnostic analyses of prevalent failure modes. Our results reveal that all three evaluator families face substantial challenges, with performance degrading sharply on long-horizon trajectories, underscoring the necessity for specialized training in agentic, trajectory-level reward modeling. Ultimately, Plan-RewardBench aims to serve as both a practical evaluation suite and a reusable blueprint for constructing agentic planning preference data.

Reinforcement learning has become essential for strengthening the reasoning abilities of large language models, yet current exploration mechanisms remain fundamentally misaligned with how these models actually learn. Entropy bonuses and external semantic comparators encourage surface level variation but offer no guarantee that sampled trajectories differ in the update directions that shape optimization. We propose G2RL, a gradient guided reinforcement learning framework in which exploration is driven not by external heuristics but by the model own first order update geometry. For each response, G2RL constructs a sequence level feature from the model final layer sensitivity, obtainable at negligible cost from a standard forward pass, and measures how each trajectory would reshape the policy by comparing these features within a sampled group. Trajectories that introduce novel gradient directions receive a bounded multiplicative reward scaler, while redundant or off manifold updates are deemphasized, yielding a self referential exploration signal that is naturally aligned with PPO style stability and KL control. Across math and general reasoning benchmarks (MATH500, AMC, AIME24, AIME25, GPQA, MMLUpro) on Qwen3 base 1.7B and 4B models, G2RL consistently improves pass@1, maj@16, and pass@k over entropy based GRPO and external embedding methods. Analyzing the induced geometry, we find that G2RL expands exploration into substantially more orthogonal and often opposing gradient directions while maintaining semantic coherence, revealing that a policy own update space provides a far more faithful and effective basis for guiding exploration in large language model reinforcement learning.

We develop a novel policy synthesis algorithm, RMPflow, based on geometrically consistent transformations of Riemannian Motion Policies (RMPs). RMPs are a class of reactive motion policies designed to parameterize non-Euclidean behaviors as dynamical systems in intrinsically nonlinear task spaces. Given a set of RMPs designed for individual tasks, RMPflow can consistently combine these local policies to generate an expressive global policy, while simultaneously exploiting sparse structure for computational efficiency. We study the geometric properties of RMPflow and provide sufficient conditions for stability. Finally, we experimentally demonstrate that accounting for the geometry of task policies can simplify classically difficult problems, such as planning through clutter on high-DOF manipulation systems.

Computer-Aided Design (CAD) plays a vital role in engineering and manufacturing, yet current CAD workflows require extensive domain expertise and manual modeling effort. Recent advances in large language models (LLMs) have made it possible to generate code from natural language, opening new opportunities for automating parametric 3D modeling. However, directly translating human design intent into executable CAD code remains highly challenging, due to the need for logical reasoning, syntactic correctness, and numerical precision. In this work, we propose CAD-RL, a multimodal Chain-of-Thought (CoT) guided reinforcement learning post training framework for CAD modeling code generation. Our method combines CoT-based Cold Start with goal-driven reinforcement learning post training using three task-specific rewards: executability reward, geometric accuracy reward, and external evaluation reward. To ensure stable policy learning under sparse and high-variance reward conditions, we introduce three targeted optimization strategies: Trust Region Stretch for improved exploration, Precision Token Loss for enhanced dimensions parameter accuracy, and Overlong Filtering to reduce noisy supervision. To support training and benchmarking, we release ExeCAD, a noval dataset comprising 16,540 real-world CAD examples with paired natural language and structured design language descriptions, executable CADQuery scripts, and rendered 3D models. Experiments demonstrate that CAD-RL achieves significant improvements in reasoning quality, output precision, and code executability over existing VLMs.

We investigate reinforcement learning (RL) for privileged planning in autonomous driving. State-of-the-art approaches for this task are rule-based, but these methods do not scale to the long tail. RL, on the other hand, is scalable and does not suffer from compounding errors like imitation learning. Contemporary RL approaches for driving use complex shaped rewards that sum multiple individual rewards, \eg~progress, position, or orientation rewards. We show that PPO fails to optimize a popular version of these rewards when the mini-batch size is increased, which limits the scalability of these approaches. Instead, we propose a new reward design based primarily on optimizing a single intuitive reward term: route completion. Infractions are penalized by terminating the episode or multiplicatively reducing route completion. We find that PPO scales well with higher mini-batch sizes when trained with our simple reward, even improving performance. Training with large mini-batch sizes enables efficient scaling via distributed data parallelism. We scale PPO to 300M samples in CARLA and 500M samples in nuPlan with a single 8-GPU node. The resulting model achieves 64 DS on the CARLA longest6 v2 benchmark, outperforming other RL methods with more complex rewards by a large margin. Requiring only minimal adaptations from its use in CARLA, the same method is the best learning-based approach on nuPlan. It scores 91.3 in non-reactive and 90.6 in reactive traffic on the Val14 benchmark while being an order of magnitude faster than prior work.

Graphical User Interface (GUI) grounding maps natural language instructions to precise interface locations for autonomous interaction. Current reinforcement learning approaches use binary rewards that treat elements as hit-or-miss targets, creating sparse signals that ignore the continuous nature of spatial interactions. Motivated by human clicking behavior that naturally forms Gaussian distributions centered on target elements, we introduce GUI Gaussian Grounding Rewards (GUI-G^2), a principled reward framework that models GUI elements as continuous Gaussian distributions across the interface plane. GUI-G^2 incorporates two synergistic mechanisms: Gaussian point rewards model precise localization through exponentially decaying distributions centered on element centroids, while coverage rewards assess spatial alignment by measuring the overlap between predicted Gaussian distributions and target regions. To handle diverse element scales, we develop an adaptive variance mechanism that calibrates reward distributions based on element dimensions. This framework transforms GUI grounding from sparse binary classification to dense continuous optimization, where Gaussian distributions generate rich gradient signals that guide models toward optimal interaction positions. Extensive experiments across ScreenSpot, ScreenSpot-v2, and ScreenSpot-Pro benchmarks demonstrate that GUI-G^2, substantially outperforms state-of-the-art method UI-TARS-72B, with the most significant improvement of 24.7% on ScreenSpot-Pro. Our analysis reveals that continuous modeling provides superior robustness to interface variations and enhanced generalization to unseen layouts, establishing a new paradigm for spatial reasoning in GUI interaction tasks.

The design of effective reward functions presents a central and often arduous challenge in reinforcement learning (RL), particularly when developing autonomous agents for complex reasoning tasks. While automated reward optimization approaches exist, they typically rely on derivative-free evolutionary heuristics that treat the reward function as a black box, failing to capture the causal relationship between reward structure and task performance. To bridge this gap, we propose Differentiable Evolutionary Reinforcement Learning (DERL), a bilevel framework that enables the autonomous discovery of optimal reward signals. In DERL, a Meta-Optimizer evolves a reward function (i.e., Meta-Reward) by composing structured atomic primitives, guiding the training of an inner-loop policy. Crucially, unlike previous evolution, DERL is differentiable in its metaoptimization: it treats the inner-loop validation performance as a signal to update the Meta-Optimizer via reinforcement learning. This allows DERL to approximate the "meta-gradient" of task success, progressively learning to generate denser and more actionable feedback. We validate DERL across three distinct domains: robotic agent (ALFWorld), scientific simulation (ScienceWorld), and mathematical reasoning (GSM8k, MATH). Experimental results show that DERL achieves state-of-the-art performance on ALFWorld and ScienceWorld, significantly outperforming methods relying on heuristic rewards, especially in out-of-distribution scenarios. Analysis of the evolutionary trajectory demonstrates that DERL successfully captures the intrinsic structure of tasks, enabling selfimproving agent alignment without human intervention.

Reward design in reinforcement learning (RL) is challenging since specifying human notions of desired behavior may be difficult via reward functions or require many expert demonstrations. Can we instead cheaply design rewards using a natural language interface? This paper explores how to simplify reward design by prompting a large language model (LLM) such as GPT-3 as a proxy reward function, where the user provides a textual prompt containing a few examples (few-shot) or a description (zero-shot) of the desired behavior. Our approach leverages this proxy reward function in an RL framework. Specifically, users specify a prompt once at the beginning of training. During training, the LLM evaluates an RL agent's behavior against the desired behavior described by the prompt and outputs a corresponding reward signal. The RL agent then uses this reward to update its behavior. We evaluate whether our approach can train agents aligned with user objectives in the Ultimatum Game, matrix games, and the DealOrNoDeal negotiation task. In all three tasks, we show that RL agents trained with our framework are well-aligned with the user's objectives and outperform RL agents trained with reward functions learned via supervised learning

Autonomous driving world models are expected to work effectively across three core dimensions: state, action, and reward. Existing models, however, are typically restricted to limited state modalities, short video sequences, imprecise action control, and a lack of reward awareness. In this paper, we introduce OmniNWM, an omniscient panoramic navigation world model that addresses all three dimensions within a unified framework. For state, OmniNWM jointly generates panoramic videos of RGB, semantics, metric depth, and 3D occupancy. A flexible forcing strategy enables high-quality long-horizon auto-regressive generation. For action, we introduce a normalized panoramic Plucker ray-map representation that encodes input trajectories into pixel-level signals, enabling highly precise and generalizable control over panoramic video generation. Regarding reward, we move beyond learning reward functions with external image-based models: instead, we leverage the generated 3D occupancy to directly define rule-based dense rewards for driving compliance and safety. Extensive experiments demonstrate that OmniNWM achieves state-of-the-art performance in video generation, control accuracy, and long-horizon stability, while providing a reliable closed-loop evaluation framework through occupancy-grounded rewards. Project page is available at https://github.com/Arlo0o/OmniNWM.

We consider algorithms for learning reward functions from human preferences over pairs of trajectory segments, as used in reinforcement learning from human feedback (RLHF). Most recent work assumes that human preferences are generated based only upon the reward accrued within those segments, or their partial return. Recent work casts doubt on the validity of this assumption, proposing an alternative preference model based upon regret. We investigate the consequences of assuming preferences are based upon partial return when they actually arise from regret. We argue that the learned function is an approximation of the optimal advantage function, A^*_r, not a reward function. We find that if a specific pitfall is addressed, this incorrect assumption is not particularly harmful, resulting in a highly shaped reward function. Nonetheless, this incorrect usage of A^*_r is less desirable than the appropriate and simpler approach of greedy maximization of A^*_r. From the perspective of the regret preference model, we also provide a clearer interpretation of fine tuning contemporary large language models with RLHF. This paper overall provides insight regarding why learning under the partial return preference model tends to work so well in practice, despite it conforming poorly to how humans give preferences.

Reward machines (RMs) are a recent formalism for representing the reward function of a reinforcement learning task through a finite-state machine whose edges encode subgoals of the task using high-level events. The structure of RMs enables the decomposition of a task into simpler and independently solvable subtasks that help tackle long-horizon and/or sparse reward tasks. We propose a formalism for further abstracting the subtask structure by endowing an RM with the ability to call other RMs, thus composing a hierarchy of RMs (HRM). We exploit HRMs by treating each call to an RM as an independently solvable subtask using the options framework, and describe a curriculum-based method to learn HRMs from traces observed by the agent. Our experiments reveal that exploiting a handcrafted HRM leads to faster convergence than with a flat HRM, and that learning an HRM is feasible in cases where its equivalent flat representation is not.

Reward engineering, the manual specification of reward functions to induce desired agent behavior, remains a fundamental challenge in multi-agent reinforcement learning. This difficulty is amplified by credit assignment ambiguity, environmental non-stationarity, and the combinatorial growth of interaction complexity. We argue that recent advances in large language models (LLMs) point toward a shift from hand-crafted numerical rewards to language-based objective specifications. Prior work has shown that LLMs can synthesize reward functions directly from natural language descriptions (e.g., EUREKA) and adapt reward formulations online with minimal human intervention (e.g., CARD). In parallel, the emerging paradigm of Reinforcement Learning from Verifiable Rewards (RLVR) provides empirical evidence that language-mediated supervision can serve as a viable alternative to traditional reward engineering. We conceptualize this transition along three dimensions: semantic reward specification, dynamic reward adaptation, and improved alignment with human intent, while noting open challenges related to computational overhead, robustness to hallucination, and scalability to large multi-agent systems. We conclude by outlining a research direction in which coordination arises from shared semantic representations rather than explicitly engineered numerical signals.

Automatically synthesizing dense rewards from natural language descriptions is a promising paradigm in reinforcement learning (RL), with applications to sparse reward problems, open-ended exploration, and hierarchical skill design. Recent works have made promising steps by exploiting the prior knowledge of large language models (LLMs). However, these approaches suffer from important limitations: they are either not scalable to problems requiring billions of environment samples, due to requiring LLM annotations for each observation, or they require a diverse offline dataset, which may not exist or be impossible to collect. In this work, we address these limitations through a combination of algorithmic and systems-level contributions. We propose \oni, a distributed architecture that simultaneously learns an RL policy and an intrinsic reward function using LLM feedback. Our approach annotates the agent's collected experience via an asynchronous LLM server, which is then distilled into an intrinsic reward model. We explore a range of algorithmic choices for reward modeling with varying complexity, including hashing, classification, and ranking models. By studying their relative tradeoffs, we shed light on questions regarding intrinsic reward design for sparse reward problems. Our approach achieves state-of-the-art performance across a range of challenging, sparse reward tasks from the NetHack Learning Environment in a simple unified process, solely using the agent's gathered experience, without requiring external datasets. We make our code available at https://github.com/facebookresearch/oni.

Exploration is essential for solving complex Reinforcement Learning (RL) tasks. Maximum State-Visitation Entropy (MSVE) formulates the exploration problem as a well-defined policy optimization problem whose solution aims at visiting all states as uniformly as possible. This is in contrast to standard uncertainty-based approaches where exploration is transient and eventually vanishes. However, existing approaches to MSVE are theoretically justified only for discrete state-spaces as they are oblivious to the geometry of continuous domains. We address this challenge by introducing Geometric Entropy Maximisation (GEM), a new algorithm that maximises the geometry-aware Shannon entropy of state-visits in both discrete and continuous domains. Our key theoretical contribution is casting geometry-aware MSVE exploration as a tractable problem of optimising a simple and novel noise-contrastive objective function. In our experiments, we show the efficiency of GEM in solving several RL problems with sparse rewards, compared against other deep RL exploration approaches.

Offline goal-conditioned reinforcement learning (GCRL) learns goal-conditioned policies from static pre-collected datasets. However, accurate value estimation remains a challenge due to the limited coverage of the state-action space. Recent physics-informed approaches have sought to address this by imposing physical and geometric constraints on the value function through regularization defined over first-order partial differential equations (PDEs), such as the Eikonal equation. However, these formulations can often be ill-posed in complex, high-dimensional environments. In this work, we propose a physics-informed regularization derived from the viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation. By providing a physics-based inductive bias, our approach grounds the learning process in optimal control theory, explicitly regularizing and bounding updates during value iterations. Furthermore, we leverage the Feynman-Kac theorem to recast the PDE solution as an expectation, enabling a tractable Monte Carlo estimation of the objective that avoids numerical instability in higher-order gradients. Experiments demonstrate that our method improves geometric consistency, making it broadly applicable to navigation and high-dimensional, complex manipulation tasks. Open-source codes are available at https://github.com/HrishikeshVish/phys-fk-value-GCRL.

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute rewards for them. The success of the traditional RL framework crucially relies on the underlying agent-reward model, which, however, depends on how accurately a system designer can express an appropriate reward function and often a non-trivial task. The main novelty of our framework is the ability to learn from preference-based trajectory feedback that eliminates the need to hand-craft numeric reward models. This paper sets up a formal framework for the PbRL problem with non-markovian rewards, where the trajectory preferences are encoded by a generalized linear model of dimension d. Assuming the transition model is known, we then propose an algorithm with almost optimal regret guarantee of mathcal{O}left( SH d log (T / delta) T right). We further, extend the above algorithm to the case of unknown transition dynamics, and provide an algorithm with near optimal regret guarantee mathcal{O}((d + H^2 + |S|)dT +|mathcal{S||A|TH} ). To the best of our knowledge, our work is one of the first to give tight regret guarantees for preference based RL problems with trajectory preferences.

While recent advances have boosted LM proficiency in linguistic benchmarks, LMs consistently struggle to reason correctly on complex tasks like mathematics. We turn to Reinforcement Learning from Human Feedback (RLHF) as a method with which to shape model reasoning processes. In particular, we explore two reward schemes, outcome-supervised reward models (ORMs) and process-supervised reward models (PRMs), to optimize for logical reasoning. Our results show that the fine-grained reward provided by PRM-based methods enhances accuracy on simple mathematical reasoning (GSM8K) while, unexpectedly, reducing performance in complex tasks (MATH). Furthermore, we show the critical role reward aggregation functions play in model performance. Providing promising avenues for future research, our study underscores the need for further exploration into fine-grained reward modeling for more reliable language models.

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging the inherent graph structure of EEG channels to capture the spatial relationships in brain activity. By exploiting task-specific symmetries, we define different pretraining strategies that not only improve model performance across all participant groups but also validate the robustness of the geometric representations. Explainability analysis based on the graph structures reveals consistent group-specific neural signatures that persist across pretraining conditions, suggesting stable geometric structures in the neural representations associated with motor learning and feedback processing. These geometric patterns exhibit partial invariance to certain task space transformations, indicating symmetries that enable generalisation across conditions while maintaining specificity to individual learning strategies. This work demonstrates how GNNs can uncover the effects of previous outcomes on motor planning, in a complex real-world task, providing insights into the geometric principles governing neural representations. Our experimental design bridges the gap between controlled experiments and ecologically valid scenarios, offering new insights into the organisation of neural representations during naturalistic motor learning, which may open avenues for exploring fundamental principles governing brain activity in complex tasks.

In the last decade, Deep Reinforcement Learning has evolved into a powerful tool for complex sequential decision-making problems. It combines deep learning's proficiency in processing rich input signals with reinforcement learning's adaptability across diverse control tasks. At its core, an RL agent seeks to maximize its cumulative reward, enabling AI algorithms to uncover novel solutions previously unknown to experts. However, this focus on reward maximization also introduces a significant difficulty: improper reward specification can result in unexpected, misaligned agent behavior and inefficient learning. The complexity of accurately specifying the reward function is further amplified by the sequential nature of the task, the sparsity of learning signals, and the multifaceted aspects of the desired behavior. In this thesis, we survey the literature on effective reward specification strategies, identify core challenges relating to each of these approaches, and propose original contributions addressing the issue of sample efficiency and alignment in deep reinforcement learning. Reward specification represents one of the most challenging aspects of applying reinforcement learning in real-world domains. Our work underscores the absence of a universal solution to this complex and nuanced challenge; solving it requires selecting the most appropriate tools for the specific requirements of each unique application.

Recent studies on post-training large language models (LLMs) for reasoning through reinforcement learning (RL) typically focus on tasks that can be accurately verified and rewarded, such as solving math problems. In contrast, our research investigates the impact of reward noise, a more practical consideration for real-world scenarios involving the post-training of LLMs using reward models. We found that LLMs demonstrate strong robustness to substantial reward noise. For example, manually flipping 40% of the reward function's outputs in math tasks still allows a Qwen-2.5-7B model to achieve rapid convergence, improving its performance on math tasks from 5% to 72%, compared to the 75% accuracy achieved by a model trained with noiseless rewards. Surprisingly, by only rewarding the appearance of key reasoning phrases (namely reasoning pattern reward, RPR), such as ``first, I need to''-without verifying the correctness of answers, the model achieved peak downstream performance (over 70% accuracy for Qwen-2.5-7B) comparable to models trained with strict correctness verification and accurate rewards. Recognizing the importance of the reasoning process over the final results, we combined RPR with noisy reward models. RPR helped calibrate the noisy reward models, mitigating potential false negatives and enhancing the LLM's performance on open-ended tasks. These findings suggest the importance of improving models' foundational abilities during the pre-training phase while providing insights for advancing post-training techniques. Our code and scripts are available at https://github.com/trestad/Noisy-Rewards-in-Learning-to-Reason.

We show that reinforcement learning with verifiable rewards (RLVR) can elicit strong mathematical reasoning in certain models even with spurious rewards that have little, no, or even negative correlation with the correct answer. For example, RLVR improves MATH-500 performance for Qwen2.5-Math-7B in absolute points by 21.4% (random reward), 13.8% (format reward), 24.1% (incorrect label), 26.0% (1-shot RL), and 27.1% (majority voting) -- nearly matching the 29.1% gained with ground truth rewards. However, the spurious rewards that work for Qwen often fail to yield gains with other model families like Llama3 or OLMo2. In particular, we find code reasoning -- thinking in code without actual code execution -- to be a distinctive Qwen2.5-Math behavior that becomes significantly more frequent after RLVR, from 65% to over 90%, even with spurious rewards. Overall, we hypothesize that, given the lack of useful reward signal, RLVR must somehow be surfacing useful reasoning representations learned during pretraining, although the exact mechanism remains a topic for future work. We suggest that future RLVR research should possibly be validated on diverse models rather than a single de facto choice, as we show that it is easy to get significant performance gains on Qwen models even with completely spurious reward signals.

Learning a precise dynamics model can be crucial for offline reinforcement learning, which, unfortunately, has been found to be quite challenging. Dynamics models that are learned by fitting historical transitions often struggle to generalize to unseen transitions. In this study, we identify a hidden but pivotal factor termed dynamics reward that remains consistent across transitions, offering a pathway to better generalization. Therefore, we propose the idea of reward-consistent dynamics models: any trajectory generated by the dynamics model should maximize the dynamics reward derived from the data. We implement this idea as the MOREC (Model-based Offline reinforcement learning with Reward Consistency) method, which can be seamlessly integrated into previous offline model-based reinforcement learning (MBRL) methods. MOREC learns a generalizable dynamics reward function from offline data, which is subsequently employed as a transition filter in any offline MBRL method: when generating transitions, the dynamics model generates a batch of transitions and selects the one with the highest dynamics reward value. On a synthetic task, we visualize that MOREC has a strong generalization ability and can surprisingly recover some distant unseen transitions. On 21 offline tasks in D4RL and NeoRL benchmarks, MOREC improves the previous state-of-the-art performance by a significant margin, i.e., 4.6% on D4RL tasks and 25.9% on NeoRL tasks. Notably, MOREC is the first method that can achieve above 95% online RL performance in 6 out of 12 D4RL tasks and 3 out of 9 NeoRL tasks.

Despite advancements in Multi-modal Large Language Models (MLLMs) for scene understanding, their performance on complex spatial reasoning tasks requiring mental simulation remains significantly limited. Current methods often rely on passive observation of spatial data, failing to internalize an active mental imagery process. To bridge this gap, we propose SpatialDreamer, a reinforcement learning framework that enables spatial reasoning through a closedloop process of active exploration, visual imagination via a world model, and evidence-grounded reasoning. To address the lack of fine-grained reward supervision in longhorizontal reasoning tasks, we propose Geometric Policy Optimization (GeoPO), which introduces tree-structured sampling and step-level reward estimation with geometric consistency constraints. Extensive experiments demonstrate that SpatialDreamer delivers highly competitive results across multiple challenging benchmarks, signifying a critical advancement in human-like active spatial mental simulation for MLLMs.

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

Large Language Models (LLMs) have shown significant potential in designing reward functions for Reinforcement Learning (RL) tasks. However, obtaining high-quality reward code often involves human intervention, numerous LLM queries, or repetitive RL training. To address these issues, we propose CARD, a LLM-driven Reward Design framework that iteratively generates and improves reward function code. Specifically, CARD includes a Coder that generates and verifies the code, while a Evaluator provides dynamic feedback to guide the Coder in improving the code, eliminating the need for human feedback. In addition to process feedback and trajectory feedback, we introduce Trajectory Preference Evaluation (TPE), which evaluates the current reward function based on trajectory preferences. If the code fails the TPE, the Evaluator provides preference feedback, avoiding RL training at every iteration and making the reward function better aligned with the task objective. Empirical results on Meta-World and ManiSkill2 demonstrate that our method achieves an effective balance between task performance and token efficiency, outperforming or matching the baselines across all tasks. On 10 out of 12 tasks, CARD shows better or comparable performance to policies trained with expert-designed rewards, and our method even surpasses the oracle on 3 tasks.

In this work, we study the simple yet universally applicable case of reward shaping in value-based Deep Reinforcement Learning (DRL). We show that reward shifting in the form of the linear transformation is equivalent to changing the initialization of the Q-function in function approximation. Based on such an equivalence, we bring the key insight that a positive reward shifting leads to conservative exploitation, while a negative reward shifting leads to curiosity-driven exploration. Accordingly, conservative exploitation improves offline RL value estimation, and optimistic value estimation improves exploration for online RL. We validate our insight on a range of RL tasks and show its improvement over baselines: (1) In offline RL, the conservative exploitation leads to improved performance based on off-the-shelf algorithms; (2) In online continuous control, multiple value functions with different shifting constants can be used to tackle the exploration-exploitation dilemma for better sample efficiency; (3) In discrete control tasks, a negative reward shifting yields an improvement over the curiosity-based exploration method.

Despite the recent success of reinforcement learning in various domains, these approaches remain, for the most part, deterringly sensitive to hyper-parameters and are often riddled with essential engineering feats allowing their success. We consider the case of off-policy generative adversarial imitation learning, and perform an in-depth review, qualitative and quantitative, of the method. We show that forcing the learned reward function to be local Lipschitz-continuous is a sine qua non condition for the method to perform well. We then study the effects of this necessary condition and provide several theoretical results involving the local Lipschitzness of the state-value function. We complement these guarantees with empirical evidence attesting to the strong positive effect that the consistent satisfaction of the Lipschitzness constraint on the reward has on imitation performance. Finally, we tackle a generic pessimistic reward preconditioning add-on spawning a large class of reward shaping methods, which makes the base method it is plugged into provably more robust, as shown in several additional theoretical guarantees. We then discuss these through a fine-grained lens and share our insights. Crucially, the guarantees derived and reported in this work are valid for any reward satisfying the Lipschitzness condition, nothing is specific to imitation. As such, these may be of independent interest.

We investigate the mechanism design problem faced by a principal who hires multiple agents to gather and report costly information. Then, the principal exploits the information to make an informed decision. We model this problem as a game, where the principal announces a mechanism consisting in action recommendations and a payment function, a.k.a. scoring rule. Then, each agent chooses an effort level and receives partial information about an underlying state of nature based on the effort. Finally, the agents report the information (possibly non-truthfully), the principal takes a decision based on this information, and the agents are paid according to the scoring rule. While previous work focuses on single-agent problems, we consider multi-agents settings. This poses the challenge of coordinating the agents' efforts and aggregating correlated information. Indeed, we show that optimal mechanisms must correlate agents' efforts, which introduces externalities among the agents, and hence complex incentive compatibility constraints and equilibrium selection problems. First, we design a polynomial-time algorithm to find an optimal incentive compatible mechanism. Then, we study an online problem, where the principal repeatedly interacts with a group of unknown agents. We design a no-regret algorithm that provides mathcal{O}(T^{2/3}) regret with respect to an optimal mechanism, matching the state-of-the-art bound for single-agent settings.

Most algorithms in reinforcement learning (RL) require that the objective is formalised with a Markovian reward function. However, it is well-known that certain tasks cannot be expressed by means of an objective in the Markov rewards formalism, motivating the study of alternative objective-specification formalisms in RL such as Linear Temporal Logic and Multi-Objective Reinforcement Learning. To date, there has not yet been any thorough analysis of how these formalisms relate to each other in terms of their expressivity. We fill this gap in the existing literature by providing a comprehensive comparison of 17 salient objective-specification formalisms. We place these formalisms in a preorder based on their expressive power, and present this preorder as a Hasse diagram. We find a variety of limitations for the different formalisms, and argue that no formalism is both dominantly expressive and straightforward to optimise with current techniques. For example, we prove that each of Regularised RL, (Outer) Nonlinear Markov Rewards, Reward Machines, Linear Temporal Logic, and Limit Average Rewards can express a task that the others cannot. The significance of our results is twofold. First, we identify important expressivity limitations to consider when specifying objectives for policy optimization. Second, our results highlight the need for future research which adapts reward learning to work with a greater variety of formalisms, since many existing reward learning methods assume that the desired objective takes a Markovian form. Our work contributes towards a more cohesive understanding of the costs and benefits of different RL objective-specification formalisms.

Traditionally, reward models used for reinforcement learning from human feedback (RLHF) are trained to directly predict preference scores without leveraging the generation capabilities of the underlying large language model (LLM). This limits the capabilities of reward models as they must reason implicitly about the quality of a response, i.e., preference modeling must be performed in a single forward pass through the model. To enable reward models to reason explicitly about the quality of a response, we introduce Critique-out-Loud (CLoud) reward models. CLoud reward models operate by first generating a natural language critique of the assistant's response that is then used to predict a scalar reward for the quality of the response. We demonstrate the success of CLoud reward models for both Llama-3-8B and 70B base models: compared to classic reward models CLoud reward models improve pairwise preference classification accuracy on RewardBench by 4.65 and 5.84 percentage points for the 8B and 70B base models respectively. Furthermore, CLoud reward models lead to a Pareto improvement for win rate on ArenaHard when used as the scoring model for Best-of-N. Finally, we explore how to exploit the dynamic inference compute capabilities of CLoud reward models by performing self-consistency decoding for reward prediction.

Ensuring sufficient exploration is a central challenge when training meta-reinforcement learning (meta-RL) agents to solve novel environments. Conventional solutions to the exploration-exploitation dilemma inject explicit incentives such as randomization, uncertainty bonuses, or intrinsic rewards to encourage exploration. In this work, we hypothesize that an agent trained solely to maximize a greedy (exploitation-only) objective can nonetheless exhibit emergent exploratory behavior, provided three conditions are met: (1) Recurring Environmental Structure, where the environment features repeatable regularities that allow past experience to inform future choices; (2) Agent Memory, enabling the agent to retain and utilize historical interaction data; and (3) Long-Horizon Credit Assignment, where learning propagates returns over a time frame sufficient for the delayed benefits of exploration to inform current decisions. Through experiments in stochastic multi-armed bandits and temporally extended gridworlds, we observe that, when both structure and memory are present, a policy trained on a strictly greedy objective exhibits information-seeking exploratory behavior. We further demonstrate, through controlled ablations, that emergent exploration vanishes if either environmental structure or agent memory is absent (Conditions 1 & 2). Surprisingly, removing long-horizon credit assignment (Condition 3) does not always prevent emergent exploration-a result we attribute to the pseudo-Thompson Sampling effect. These findings suggest that, under the right prerequisites, exploration and exploitation need not be treated as orthogonal objectives but can emerge from a unified reward-maximization process.

Recent studies have demonstrated significant progress in aligning text-to-image diffusion models with human preference via Reinforcement Learning from Human Feedback. However, while existing methods achieve high scores on automated reward metrics, they often lead to Preference Mode Collapse (PMC)-a specific form of reward hacking where models converge on narrow, high-scoring outputs (e.g., images with monolithic styles or pervasive overexposure), severely degrading generative diversity. In this work, we introduce and quantify this phenomenon, proposing DivGenBench, a novel benchmark designed to measure the extent of PMC. We posit that this collapse is driven by over-optimization along the reward model's inherent biases. Building on this analysis, we propose Directional Decoupling Alignment (D^2-Align), a novel framework that mitigates PMC by directionally correcting the reward signal. Specifically, our method first learns a directional correction within the reward model's embedding space while keeping the model frozen. This correction is then applied to the reward signal during the optimization process, preventing the model from collapsing into specific modes and thereby maintaining diversity. Our comprehensive evaluation, combining qualitative analysis with quantitative metrics for both quality and diversity, reveals that D^2-Align achieves superior alignment with human preference.

Graphical user interface (GUI) agents are rapidly progressing toward autonomous interaction and reliable task execution across diverse applications. However, two central challenges remain unresolved: automating the evaluation of agent trajectories and generating high-quality training data at scale to enable continual improvement. Existing approaches often depend on manual annotation or static rule-based verification, which restricts scalability and limits adaptability in dynamic environments. We present MagicGUI-RMS, a multi-agent reward model system that delivers adaptive trajectory evaluation, corrective feedback, and self-evolving learning capabilities. MagicGUI-RMS integrates a Domain-Specific Reward Model (DS-RM) with a General-Purpose Reward Model (GP-RM), enabling fine-grained action assessment and robust generalization across heterogeneous GUI tasks. To support reward learning at scale, we design a structured data construction pipeline that automatically produces balanced and diverse reward datasets, effectively reducing annotation costs while maintaining sample fidelity. During execution, the reward model system identifies erroneous actions, proposes refined alternatives, and continuously enhances agent behavior through an automated data-reflux mechanism. Extensive experiments demonstrate that MagicGUI-RMS yields substantial gains in task accuracy, behavioral robustness. These results establish MagicGUI-RMS as a principled and effective foundation for building self-improving GUI agents driven by reward-based adaptation.

A well-designed reward is critical for effective reinforcement learning-based policy improvement. In real-world robotic domains, obtaining such rewards typically requires either labor-intensive human labeling or brittle, handcrafted objectives. Vision-language models (VLMs) have shown promise as automatic reward models, yet their effectiveness on real robot tasks is poorly understood. In this work, we aim to close this gap by introducing (1) RoboReward, a robotics reward dataset and benchmark built on large-scale real-robot corpora from Open X-Embodiment (OXE) and RoboArena, and (2) vision-language reward models trained on this dataset (RoboReward 4B/8B). Because OXE is success-heavy and lacks failure examples, we propose a negative examples data augmentation pipeline that generates calibrated negatives and near-misses via counterfactual relabeling of successful episodes and temporal clipping to create partial-progress outcomes from the same videos. Using this framework, we produce an extensive training and evaluation dataset that spans diverse tasks and embodiments and enables systematic evaluation of whether state-of-the-art VLMs can reliably provide rewards for robotics. Our evaluation of leading open-weight and proprietary VLMs reveals that no model excels across all tasks, underscoring substantial room for improvement. We then train general-purpose 4B- and 8B-parameter models that outperform much larger VLMs in assigning rewards for short-horizon robotic tasks. Finally, we deploy the 8B-parameter reward VLM in real-robot reinforcement learning and find that it improves policy learning over Gemini Robotics-ER 1.5, a frontier physical reasoning VLM trained on robotics data, by a large margin, while substantially narrowing the gap to RL training with human-provided rewards.

Vision-Language Models (VLMs) have shown remarkable capabilities in spatial reasoning, yet they remain fundamentally limited to qualitative precision and lack the computational precision required for real-world robotics. Current approaches fail to leverage metric cues from depth sensors and camera calibration, instead reducing geometric problems to pattern recognition tasks that cannot deliver the centimeter-level accuracy essential for robotic manipulation. We present TIGeR (Tool-Integrated Geometric Reasoning), a novel framework that transforms VLMs from perceptual estimators to geometric computers by enabling them to generate and execute precise geometric computations through external tools. Rather than attempting to internalize complex geometric operations within neural networks, TIGeR empowers models to recognize geometric reasoning requirements, synthesize appropriate computational code, and invoke specialized libraries for exact calculations. To support this paradigm, we introduce TIGeR-300K, a comprehensive tool-invocation-oriented dataset covering point transformations, pose estimation, and spatial compatibility verification, complete with tool invocation sequences and intermediate computations. Through a two-stage training pipeline combining supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT) with our proposed hierarchical reward design, TIGeR achieves SOTA performance on geometric reasoning benchmarks while demonstrating centimeter-level precision in real-world robotic manipulation tasks.

We study a strategic variant of the multi-armed bandit problem, which we coin the strategic click-bandit. This model is motivated by applications in online recommendation where the choice of recommended items depends on both the click-through rates and the post-click rewards. Like in classical bandits, rewards follow a fixed unknown distribution. However, we assume that the click-rate of each arm is chosen strategically by the arm (e.g., a host on Airbnb) in order to maximize the number of times it gets clicked. The algorithm designer does not know the post-click rewards nor the arms' actions (i.e., strategically chosen click-rates) in advance, and must learn both values over time. To solve this problem, we design an incentive-aware learning algorithm, UCB-S, which achieves two goals simultaneously: (a) incentivizing desirable arm behavior under uncertainty; (b) minimizing regret by learning unknown parameters. We characterize all approximate Nash equilibria among arms under UCB-S and show a mathcal{O} (KT) regret bound uniformly in every equilibrium. We also show that incentive-unaware algorithms generally fail to achieve low regret in the strategic click-bandit. Finally, we support our theoretical results by simulations of strategic arm behavior which confirm the effectiveness and robustness of our proposed incentive design.

We present HSImul3R, a unified framework for simulation-ready 3D reconstruction of human-scene interactions (HSI) from casual captures, including sparse-view images and monocular videos. Existing methods suffer from a perception-simulation gap: visually plausible reconstructions often violate physical constraints, leading to instability in physics engines and failure in embodied AI applications. To bridge this gap, we introduce a physically-grounded bi-directional optimization pipeline that treats the physics simulator as an active supervisor to jointly refine human dynamics and scene geometry. In the forward direction, we employ Scene-targeted Reinforcement Learning to optimize human motion under dual supervision of motion fidelity and contact stability. In the reverse direction, we propose Direct Simulation Reward Optimization, which leverages simulation feedback on gravitational stability and interaction success to refine scene geometry. We further present HSIBench, a new benchmark with diverse objects and interaction scenarios. Extensive experiments demonstrate that HSImul3R produces the first stable, simulation-ready HSI reconstructions and can be directly deployed to real-world humanoid robots.

Energy-based predictive world models provide a powerful approach for multi-step visual planning by reasoning over latent energy landscapes rather than generating pixels. However, existing approaches face two major challenges: (i) their latent representations are typically learned in Euclidean space, neglecting the underlying geometric and hierarchical structure among states, and (ii) they struggle with long-horizon prediction, which leads to rapid degradation across extended rollouts. To address these challenges, we introduce GeoWorld, a geometric world model that preserves geometric structure and hierarchical relations through a Hyperbolic JEPA, which maps latent representations from Euclidean space onto hyperbolic manifolds. We further introduce Geometric Reinforcement Learning for energy-based optimization, enabling stable multi-step planning in hyperbolic latent space. Extensive experiments on CrossTask and COIN demonstrate around 3% SR improvement in 3-step planning and 2% SR improvement in 4-step planning compared to the state-of-the-art V-JEPA 2. Project website: https://steve-zeyu-zhang.github.io/GeoWorld.

Reward specification plays a central role in reinforcement learning (RL), guiding the agent's behavior. To express non-Markovian rewards, formalisms such as reward machines have been introduced to capture dependencies on histories. However, traditional reward machines lack the ability to model precise timing constraints, limiting their use in time-sensitive applications. In this paper, we propose timed reward machines (TRMs), which are an extension of reward machines that incorporate timing constraints into the reward structure. TRMs enable more expressive specifications with tunable reward logic, for example, imposing costs for delays and granting rewards for timely actions. We study model-free RL frameworks (i.e., tabular Q-learning) for learning optimal policies with TRMs under digital and real-time semantics. Our algorithms integrate the TRM into learning via abstractions of timed automata, and employ counterfactual-imagining heuristics that exploit the structure of the TRM to improve the search. Experimentally, we demonstrate that our algorithm learns policies that achieve high rewards while satisfying the timing constraints specified by the TRM on popular RL benchmarks. Moreover, we conduct comparative studies of performance under different TRM semantics, along with ablations that highlight the benefits of counterfactual-imagining.

In many real-world scenarios, rewards extrinsic to the agent are extremely sparse, or absent altogether. In such cases, curiosity can serve as an intrinsic reward signal to enable the agent to explore its environment and learn skills that might be useful later in its life. We formulate curiosity as the error in an agent's ability to predict the consequence of its own actions in a visual feature space learned by a self-supervised inverse dynamics model. Our formulation scales to high-dimensional continuous state spaces like images, bypasses the difficulties of directly predicting pixels, and, critically, ignores the aspects of the environment that cannot affect the agent. The proposed approach is evaluated in two environments: VizDoom and Super Mario Bros. Three broad settings are investigated: 1) sparse extrinsic reward, where curiosity allows for far fewer interactions with the environment to reach the goal; 2) exploration with no extrinsic reward, where curiosity pushes the agent to explore more efficiently; and 3) generalization to unseen scenarios (e.g. new levels of the same game) where the knowledge gained from earlier experience helps the agent explore new places much faster than starting from scratch. Demo video and code available at https://pathak22.github.io/noreward-rl/

Learning from feedback is an instrumental process for advancing the capabilities and safety of frontier models, yet its effectiveness is often constrained by cost and scalability. We present a pilot study that explores scaling reward models through unsupervised approaches. We operationalize reward-based scaling (RBS), in its simplest form, as preference learning over document prefixes and suffixes drawn from large-scale web corpora. Its advantage is demonstrated in various aspects: despite using no human annotations, training on 11M tokens of math-focused web data yields steady gains on RewardBench v1 and v2, and these improvements consistently transfer across diverse initialization backbones spanning model families and scales. Across models, our method improves RewardBench v2 accuracy by up to +7.7 points on average, with gains of up to +16.1 on in-domain math subsets and consistent improvements on out-of-domain safety and general subsets. When applied to best-of-N selection and policy optimization, these reward models substantially improve downstream math performance and match or exceed strong supervised reward model baselines of similar size. Overall, we demonstrate the feasibility and promise of training reward models without costly and potentially unreliable human annotations.

Designing rewards for Reinforcement Learning (RL) is challenging because it needs to convey the desired task, be efficient to optimize, and be easy to compute. The latter is particularly problematic when applying RL to robotics, where detecting whether the desired configuration is reached might require considerable supervision and instrumentation. Furthermore, we are often interested in being able to reach a wide range of configurations, hence setting up a different reward every time might be unpractical. Methods like Hindsight Experience Replay (HER) have recently shown promise to learn policies able to reach many goals, without the need of a reward. Unfortunately, without tricks like resetting to points along the trajectory, HER might require many samples to discover how to reach certain areas of the state-space. In this work we investigate different approaches to incorporate demonstrations to drastically speed up the convergence to a policy able to reach any goal, also surpassing the performance of an agent trained with other Imitation Learning algorithms. Furthermore, we show our method can also be used when the available expert trajectories do not contain the actions, which can leverage kinesthetic or third person demonstration. The code is available at https://sites.google.com/view/goalconditioned-il/.

Reinforcement learning (RL) has become a standard approach for post-training large language models and, more recently, for improving image generation models, which uses reward functions to enhance generation quality and human preference alignment. However, existing reward designs are often imperfect proxies for true human judgment, making models prone to reward hacking--producing unrealistic or low-quality images that nevertheless achieve high reward scores. In this work, we systematically analyze reward hacking behaviors in text-to-image (T2I) RL post-training. We investigate how both aesthetic/human preference rewards and prompt-image consistency rewards individually contribute to reward hacking and further show that ensembling multiple rewards can only partially mitigate this issue. Across diverse reward models, we identify a common failure mode: the generation of artifact-prone images. To address this, we propose a lightweight and adaptive artifact reward model, trained on a small curated dataset of artifact-free and artifact-containing samples. This model can be integrated into existing RL pipelines as an effective regularizer for commonly used reward models. Experiments demonstrate that incorporating our artifact reward significantly improves visual realism and reduces reward hacking across multiple T2I RL setups, demonstrating the effectiveness of lightweight reward augment serving as a safeguard against reward hacking.

Consider the problem of exploration in sparse-reward or reward-free environments, such as in Montezuma's Revenge. In the curiosity-driven paradigm, the agent is rewarded for how much each realized outcome differs from their predicted outcome. But using predictive error as intrinsic motivation is fragile in stochastic environments, as the agent may become trapped by high-entropy areas of the state-action space, such as a "noisy TV". In this work, we study a natural solution derived from structural causal models of the world: Our key idea is to learn representations of the future that capture precisely the unpredictable aspects of each outcome -- which we use as additional input for predictions, such that intrinsic rewards only reflect the predictable aspects of world dynamics. First, we propose incorporating such hindsight representations into models to disentangle "noise" from "novelty", yielding Curiosity in Hindsight: a simple and scalable generalization of curiosity that is robust to stochasticity. Second, we instantiate this framework for the recently introduced BYOL-Explore algorithm as our prime example, resulting in the noise-robust BYOL-Hindsight. Third, we illustrate its behavior under a variety of different stochasticities in a grid world, and find improvements over BYOL-Explore in hard-exploration Atari games with sticky actions. Notably, we show state-of-the-art results in exploring Montezuma's Revenge with sticky actions, while preserving performance in the non-sticky setting.

Large language models (LLMs) excel at program synthesis, yet their ability to produce symbolic graphics programs (SGPs) that render into precise visual content remains underexplored. We study symbolic graphics programming, where the goal is to generate an SGP from a natural-language description. This task also serves as a lens into how LLMs understand the visual world by prompting them to generate images rendered from SGPs. Among various SGPs, our paper sticks to scalable vector graphics (SVGs). We begin by examining the extent to which LLMs can generate SGPs. To this end, we introduce SGP-GenBench, a comprehensive benchmark covering object fidelity, scene fidelity, and compositionality (attribute binding, spatial relations, numeracy). On SGP-GenBench, we discover that frontier proprietary models substantially outperform open-source models, and performance correlates well with general coding capabilities. Motivated by this gap, we aim to improve LLMs' ability to generate SGPs. We propose a reinforcement learning (RL) with verifiable rewards approach, where a format-validity gate ensures renderable SVG, and a cross-modal reward aligns text and the rendered image via strong vision encoders (e.g., SigLIP for text-image and DINO for image-image). Applied to Qwen-2.5-7B, our method substantially improves SVG generation quality and semantics, achieving performance on par with frontier systems. We further analyze training dynamics, showing that RL induces (i) finer decomposition of objects into controllable primitives and (ii) contextual details that improve scene coherence. Our results demonstrate that symbolic graphics programming offers a precise and interpretable lens on cross-modal grounding.

Effective reward design is a central challenge in Reinforcement Learning (RL) for code generation. Mainstream pass/fail outcome rewards enforce functional correctness via executing unit tests, but the resulting sparsity limits potential performance gains. While recent work has explored external Reward Models (RM) to generate richer, continuous rewards, the learned RMs suffer from reward misalignment and prohibitive computational cost. In this paper, we introduce VeRPO (Verifiable Dense Reward Policy Optimization), a novel RL framework for code generation that synthesizes robust and dense rewards fully grounded in verifiable execution feedback. The core idea of VeRPO is constructing dense rewards from weighted partial success: by dynamically estimating the difficulty weight of each unit test based on the execution statistics during training, a dense reward is derived from the sum of weights of the passed unit tests. To solidify the consistency between partial success and end-to-end functional correctness, VeRPO further integrates the dense signal with global execution outcomes, establishing a robust and dense reward paradigm relying solely on verifiable execution feedback. Extensive experiments across diverse benchmarks and settings demonstrate that VeRPO consistently outperforms outcome-driven and RM-based baselines, achieving up to +8.83\% gain in pass@1 with negligible time cost (< 0.02\%) and zero GPU memory overhead.

A reliable reward function is essential for reinforcement learning (RL) in image generation. Most current RL approaches depend on pre-trained preference models that output scalar rewards to approximate human preferences. However, these rewards often fail to capture human perception and are vulnerable to reward hacking, where higher scores do not correspond to better images. To address this, we introduce Adv-GRPO, an RL framework with an adversarial reward that iteratively updates both the reward model and the generator. The reward model is supervised using reference images as positive samples and can largely avoid being hacked. Unlike KL regularization that constrains parameter updates, our learned reward directly guides the generator through its visual outputs, leading to higher-quality images. Moreover, while optimizing existing reward functions can alleviate reward hacking, their inherent biases remain. For instance, PickScore may degrade image quality, whereas OCR-based rewards often reduce aesthetic fidelity. To address this, we take the image itself as a reward, using reference images and vision foundation models (e.g., DINO) to provide rich visual rewards. These dense visual signals, instead of a single scalar, lead to consistent gains across image quality, aesthetics, and task-specific metrics. Finally, we show that combining reference samples with foundation-model rewards enables distribution transfer and flexible style customization. In human evaluation, our method outperforms Flow-GRPO and SD3, achieving 70.0% and 72.4% win rates in image quality and aesthetics, respectively. Code and models have been released.

Reinforcement learning (RL) algorithms aim to balance exploiting the current best strategy with exploring new options that could lead to higher rewards. Most common RL algorithms use undirected exploration, i.e., select random sequences of actions. Exploration can also be directed using intrinsic rewards, such as curiosity or model epistemic uncertainty. However, effectively balancing task and intrinsic rewards is challenging and often task-dependent. In this work, we introduce a framework, MaxInfoRL, for balancing intrinsic and extrinsic exploration. MaxInfoRL steers exploration towards informative transitions, by maximizing intrinsic rewards such as the information gain about the underlying task. When combined with Boltzmann exploration, this approach naturally trades off maximization of the value function with that of the entropy over states, rewards, and actions. We show that our approach achieves sublinear regret in the simplified setting of multi-armed bandits. We then apply this general formulation to a variety of off-policy model-free RL methods for continuous state-action spaces, yielding novel algorithms that achieve superior performance across hard exploration problems and complex scenarios such as visual control tasks.

In this work, we study the issue of reward hacking on the response length, a challenge emerging in Reinforcement Learning from Human Feedback (RLHF) on LLMs. A well-formatted, verbose but less helpful response from the LLMs can often deceive LLMs or even human evaluators to achieve high scores. The same issue also holds for some reward models in RL. To address the challenges in both training and evaluation, we establish a more reliable evaluation protocol for comparing different training configurations, which inspects the trade-off between LLM evaluation score and response length obtained by varying training hyperparameters. Based on this evaluation, we conduct large-scale studies, where the results shed insights into the efficacy of hyperparameters and tricks used in RL on mitigating length bias. We further propose to improve the reward model by jointly training two linear heads on shared feature representations to predict the rewards, one trained to correlate with length, and the other trained to decorrelate with length and therefore focus more on the actual content. We then discard the length head in RL to prevent reward hacking on length. Experiments demonstrate that our approach almost eliminates the reward correlation with length, and improves the obtained policy by a significant margin.

The discovery of extremal structures in mathematics requires navigating vast and nonconvex landscapes where analytical methods offer little guidance and brute-force search becomes intractable. We introduce FlowBoost, a closed-loop generative framework that learns to discover rare and extremal geometric structures by combining three components: (i) a geometry-aware conditional flow-matching model that learns to sample high-quality configurations, (ii) reward-guided policy optimization with action exploration that directly optimizes the generation process toward the objective while maintaining diversity, and (iii) stochastic local search for both training-data generation and final refinement. Unlike prior open-loop approaches, such as PatternBoost that retrains on filtered discrete samples, or AlphaEvolve which relies on frozen Large Language Models (LLMs) as evolutionary mutation operators, FlowBoost enforces geometric feasibility during sampling, and propagates reward signal directly into the generative model, closing the optimization loop and requiring much smaller training sets and shorter training times, and reducing the required outer-loop iterations by orders of magnitude, while eliminating dependence on LLMs. We demonstrate the framework on four geometric optimization problems: sphere packing in hypercubes, circle packing maximizing sum of radii, the Heilbronn triangle problem, and star discrepancy minimization. In several cases, FlowBoost discovers configurations that match or exceed the best known results. For circle packings, we improve the best known lower bounds, surpassing the LLM-based system AlphaEvolve while using substantially fewer computational resources.

Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Recent attempts construct auxiliary lines via code-driven rendering, a strategy that relies on accurate and executable code generation to produce visual renderings of the auxiliary lines for subsequent reasoning. However, in complex solid geometry settings, such a strong dependence on precise specifications substantially restricts the robustness of this strategy. Alternatively, we turn to a simpler and more stable solution, representing auxiliary-line constructions as structured textual descriptions. To bridge the gap between textual descriptions and spatial structure, we propose a reinforcement learning framework that enhances diagram-text alignment. The core is a cross-modal reward model that evaluates how well the generated auxiliary-line description matches the ground-truth auxiliary-line diagram. The reward signal drives a GRPO-based RL stage to yield informative auxiliary-line descriptions for the reasoning. To support the training and evaluation, we develop a scalable data pipeline and construct AuxSolidMath, a dataset of 3,018 real-exam geometry problems with paired diagrams and aligned textual fields. Based on this framework, we derive GeoVLMath, an LVLM for solving complex solid geometry.

Diffusion models have emerged as the de facto paradigm for video generation. However, their reliance on web-scale data of varied quality often yields results that are visually unappealing and misaligned with the textual prompts. To tackle this problem, we propose InstructVideo to instruct text-to-video diffusion models with human feedback by reward fine-tuning. InstructVideo has two key ingredients: 1) To ameliorate the cost of reward fine-tuning induced by generating through the full DDIM sampling chain, we recast reward fine-tuning as editing. By leveraging the diffusion process to corrupt a sampled video, InstructVideo requires only partial inference of the DDIM sampling chain, reducing fine-tuning cost while improving fine-tuning efficiency. 2) To mitigate the absence of a dedicated video reward model for human preferences, we repurpose established image reward models, e.g., HPSv2. To this end, we propose Segmental Video Reward, a mechanism to provide reward signals based on segmental sparse sampling, and Temporally Attenuated Reward, a method that mitigates temporal modeling degradation during fine-tuning. Extensive experiments, both qualitative and quantitative, validate the practicality and efficacy of using image reward models in InstructVideo, significantly enhancing the visual quality of generated videos without compromising generalization capabilities. Code and models will be made publicly available.

Reinforcement learning (RL) in long horizon and sparse reward tasks is notoriously difficult and requires a lot of training steps. A standard solution to speed up the process is to leverage additional reward signals, shaping it to better guide the learning process. In the context of language-conditioned RL, the abstraction and generalisation properties of the language input provide opportunities for more efficient ways of shaping the reward. In this paper, we leverage this idea and propose an automated reward shaping method where the agent extracts auxiliary objectives from the general language goal. These auxiliary objectives use a question generation (QG) and question answering (QA) system: they consist of questions leading the agent to try to reconstruct partial information about the global goal using its own trajectory. When it succeeds, it receives an intrinsic reward proportional to its confidence in its answer. This incentivizes the agent to generate trajectories which unambiguously explain various aspects of the general language goal. Our experimental study shows that this approach, which does not require engineer intervention to design the auxiliary objectives, improves sample efficiency by effectively directing exploration.

360 panoramic images are increasingly used in virtual reality, autonomous driving, and robotics for holistic scene understanding. However, current Vision-Language Models (VLMs) struggle with 3D spatial reasoning on Equirectangular Projection (ERP) images due to geometric distortion and limited 3D supervision. We introduce PanoEnv, a large-scale VQA benchmark built from synthetic 3D environments, containing 14.8K questions across five categories (e.g., relative position, volume comparison) grounded in accurate 3D annotations including depth, segmentation, and bounding boxes. Benchmarking 14 state-of-the-art VLMs reveals limited 3D understanding, achieving only 49.34% overall accuracy and 8.36% on open-ended (OE) questions. To enhance 3D reasoning, we propose a reinforcement learning post-training framework based on Group Relative Policy Optimization (GRPO) with a ground-truth-guided reward that incorporates five geometry-aware strategies such as distance tolerance and spatial consistency. A two-stage curriculum further mitigates catastrophic forgetting: Stage 1 trains on structured tasks (true/false and multiple choice), and Stage 2 fine-tunes on mixed open-ended data to improve generalization. Our 7B model achieves new state-of-the-art performance, improving overall accuracy to 52.93% (+3.59%) and open-ended accuracy to 14.83% while maintaining structured-task performance. It also achieves top semantic evaluation scores (Q-Score 6.24, P-Score 5.95), surpassing 32B models. These results demonstrate that PanoEnv-QA and our curriculum-based RL framework effectively instill 3D spatial intelligence in VLMs for omnidirectional perception.

Offline Reinforcement Learning (ORL) offers a robust solution to training agents in applications where interactions with the environment must be strictly limited due to cost, safety, or lack of accurate simulation environments. Despite its potential to facilitate deployment of artificial agents in the real world, Offline Reinforcement Learning typically requires very many demonstrations annotated with ground-truth rewards. Consequently, state-of-the-art ORL algorithms can be difficult or impossible to apply in data-scarce scenarios. In this paper we propose a simple but effective Reward Model that can estimate the reward signal from a very limited sample of environment transitions annotated with rewards. Once the reward signal is modeled, we use the Reward Model to impute rewards for a large sample of reward-free transitions, thus enabling the application of ORL techniques. We demonstrate the potential of our approach on several D4RL continuous locomotion tasks. Our results show that, using only 1\% of reward-labeled transitions from the original datasets, our learned reward model is able to impute rewards for the remaining 99\% of the transitions, from which performant agents can be learned using Offline Reinforcement Learning.

In the absence of extensive human-annotated data for complex reasoning tasks, self-improvement -- where models are trained on their own outputs -- has emerged as a primary method for enhancing performance. However, the critical factors underlying the mechanism of these iterative self-improving methods remain poorly understood, such as under what conditions self-improvement is effective, and what are the bottlenecks in the current iterations. In this work, we identify and propose methods to monitor two pivotal factors in this iterative process: (1) the model's ability to generate sufficiently diverse responses (exploration); and (2) the effectiveness of external rewards in distinguishing high-quality candidates from lower-quality ones (exploitation). Using mathematical reasoning as a case study, we begin with a quantitative analysis to track the dynamics of exploration and exploitation, discovering that a model's exploratory capabilities rapidly deteriorate over iterations, and the effectiveness of exploiting external rewards diminishes as well. Motivated by these findings, we introduce B-STaR, a Self-Taught Reasoning framework that autonomously adjusts configurations across iterations to Balance exploration and exploitation, thereby optimizing the self-improving effectiveness based on the current policy model and available rewards. Our experiments on mathematical reasoning, coding, and commonsense reasoning demonstrate that B-STaR not only enhances the model's exploratory capabilities throughout training but also achieves a more effective balance between exploration and exploitation, leading to superior performance.

Reinforcement learning has delivered promising results in achieving human- or even superhuman-level capabilities across diverse problem domains, but success in dexterous robot manipulation remains limited. This work investigates the key challenges in applying reinforcement learning to solve a collection of contact-rich manipulation tasks on a humanoid embodiment. We introduce novel techniques to overcome the identified challenges with empirical validation. Our main contributions include an automated real-to-sim tuning module that brings the simulated environment closer to the real world, a generalized reward design scheme that simplifies reward engineering for long-horizon contact-rich manipulation tasks, a divide-and-conquer distillation process that improves the sample efficiency of hard-exploration problems while maintaining sim-to-real performance, and a mixture of sparse and dense object representations to bridge the sim-to-real perception gap. We show promising results on three humanoid dexterous manipulation tasks, with ablation studies on each technique. Our work presents a successful approach to learning humanoid dexterous manipulation using sim-to-real reinforcement learning, achieving robust generalization and high performance without the need for human demonstration.

Aligning multimodal large language models (MLLMs) with human preferences often relies on single-signal, model-based reward methods. Such monolithic rewards often lack confidence calibration across domain-specific tasks, fail to capture diverse aspects of human preferences, and require extensive data annotation and reward model training. In this work, we propose a hybrid reward modeling framework that integrates complementary reward paradigms: (i) model-based rewards, where a learned reward model predicts scalar or vector scores from synthetic and human feedback, and (ii) rule-based rewards, where domain-specific heuristics provide explicit correctness signals with confidence. Beyond accuracy, we further incorporate multi-aspect rewards to enforce instruction adherence and introduce a generalized length-penalty reward to stabilize training and improve performance. The proposed framework provides a flexible and effective approach to aligning MLLMs through reinforcement learning policy optimization. Our experiments show consistent improvements across different multimodal benchmarks when applying hybrid and multi-aspect reward modeling. Our best performing model in the 3B family achieves an overall average improvement of ~9.5% across general and math reasoning tasks. Focusing specifically on mathematical benchmarks, the model achieves a significant average improvement of ~16%, highlighting its effectiveness in mathematical reasoning and problem solving.

Competitions for shareable and limited resources have long been studied with strategic agents. In reality, agents often have to learn and maximize the rewards of the resources at the same time. To design an individualized competing policy, we model the competition between agents in a novel multi-player multi-armed bandit (MPMAB) setting where players are selfish and aim to maximize their own rewards. In addition, when several players pull the same arm, we assume that these players averagely share the arms' rewards by expectation. Under this setting, we first analyze the Nash equilibrium when arms' rewards are known. Subsequently, we propose a novel SelfishMPMAB with Averaging Allocation (SMAA) approach based on the equilibrium. We theoretically demonstrate that SMAA could achieve a good regret guarantee for each player when all players follow the algorithm. Additionally, we establish that no single selfish player can significantly increase their rewards through deviation, nor can they detrimentally affect other players' rewards without incurring substantial losses for themselves. We finally validate the effectiveness of the method in extensive synthetic experiments.

Reward Models (RMs) are critical for improving generation models via Reinforcement Learning (RL), yet the RM scaling paradigm in visual generation remains largely unexplored. It primarily due to fundamental limitations in existing approaches: CLIP-based RMs suffer from architectural and input modality constraints, while prevalent Bradley-Terry losses are fundamentally misaligned with the next-token prediction mechanism of Vision-Language Models (VLMs), hindering effective scaling. More critically, the RLHF optimization process is plagued by Reward Hacking issue, where models exploit flaws in the reward signal without improving true quality. To address these challenges, we introduce RewardDance, a scalable reward modeling framework that overcomes these barriers through a novel generative reward paradigm. By reformulating the reward score as the model's probability of predicting a "yes" token, indicating that the generated image outperforms a reference image according to specific criteria, RewardDance intrinsically aligns reward objectives with VLM architectures. This alignment unlocks scaling across two dimensions: (1) Model Scaling: Systematic scaling of RMs up to 26 billion parameters; (2) Context Scaling: Integration of task-specific instructions, reference examples, and chain-of-thought (CoT) reasoning. Extensive experiments demonstrate that RewardDance significantly surpasses state-of-the-art methods in text-to-image, text-to-video, and image-to-video generation. Crucially, we resolve the persistent challenge of "reward hacking": Our large-scale RMs exhibit and maintain high reward variance during RL fine-tuning, proving their resistance to hacking and ability to produce diverse, high-quality outputs. It greatly relieves the mode collapse problem that plagues smaller models.

Reward engineering has long been a challenge in Reinforcement Learning (RL) research, as it often requires extensive human effort and iterative processes of trial-and-error to design effective reward functions. In this paper, we propose RL-VLM-F, a method that automatically generates reward functions for agents to learn new tasks, using only a text description of the task goal and the agent's visual observations, by leveraging feedbacks from vision language foundation models (VLMs). The key to our approach is to query these models to give preferences over pairs of the agent's image observations based on the text description of the task goal, and then learn a reward function from the preference labels, rather than directly prompting these models to output a raw reward score, which can be noisy and inconsistent. We demonstrate that RL-VLM-F successfully produces effective rewards and policies across various domains - including classic control, as well as manipulation of rigid, articulated, and deformable objects - without the need for human supervision, outperforming prior methods that use large pretrained models for reward generation under the same assumptions.

Recent reinforcement learning (RL) approaches have shown strong performance in complex domains such as Atari games, but are often highly sample inefficient. A common approach to reduce interaction time with the environment is to use reward shaping, which involves carefully designing reward functions that provide the agent intermediate rewards for progress towards the goal. However, designing appropriate shaping rewards is known to be difficult as well as time-consuming. In this work, we address this problem by using natural language instructions to perform reward shaping. We propose the LanguagE-Action Reward Network (LEARN), a framework that maps free-form natural language instructions to intermediate rewards based on actions taken by the agent. These intermediate language-based rewards can seamlessly be integrated into any standard reinforcement learning algorithm. We experiment with Montezuma's Revenge from the Atari Learning Environment, a popular benchmark in RL. Our experiments on a diverse set of 15 tasks demonstrate that, for the same number of interactions with the environment, language-based rewards lead to successful completion of the task 60% more often on average, compared to learning without language.

Significant progress in reward modeling over recent years has been driven by a paradigm shift from task-specific designs towards generalist reward models. Despite this trend, developing effective reward models remains a fundamental challenge: the heavy reliance on large-scale labeled preference data. Pre-training on abundant unlabeled data offers a promising direction, but existing approaches fall short of instilling explicit reasoning into reward models. To bridge this gap, we propose a self-training approach that leverages unlabeled data to elicit reward reasoning in reward models. Based on this approach, we develop GRAM-R^2, a generative reward model trained to produce not only preference labels but also accompanying reward rationales. GRAM-R^2 can serve as a foundation model for reward reasoning and can be applied to a wide range of tasks with minimal or no additional fine-tuning. It can support downstream applications such as response ranking and task-specific reward tuning. Experiments on response ranking, task adaptation, and reinforcement learning from human feedback demonstrate that GRAM-R^2 consistently delivers strong performance, outperforming several strong discriminative and generative baselines.

We present a general convergent class of reinforcement learning algorithms that is founded on two distinct principles: (1) mapping value estimates to a different space using arbitrary functions from a broad class, and (2) linearly decomposing the reward signal into multiple channels. The first principle enables incorporating specific properties into the value estimator that can enhance learning. The second principle, on the other hand, allows for the value function to be represented as a composition of multiple utility functions. This can be leveraged for various purposes, e.g. dealing with highly varying reward scales, incorporating a priori knowledge about the sources of reward, and ensemble learning. Combining the two principles yields a general blueprint for instantiating convergent algorithms by orchestrating diverse mapping functions over multiple reward channels. This blueprint generalizes and subsumes algorithms such as Q-Learning, Log Q-Learning, and Q-Decomposition. In addition, our convergence proof for this general class relaxes certain required assumptions in some of these algorithms. Based on our theory, we discuss several interesting configurations as special cases. Finally, to illustrate the potential of the design space that our theory opens up, we instantiate a particular algorithm and evaluate its performance on the Atari suite.

Recent advances in multimodal Reward Models (RMs) have shown significant promise in delivering reward signals to align vision models with human preferences. However, current RMs are generally restricted to providing direct responses or engaging in shallow reasoning processes with limited depth, often leading to inaccurate reward signals. We posit that incorporating explicit long chains of thought (CoT) into the reward reasoning process can significantly strengthen their reliability and robustness. Furthermore, we believe that once RMs internalize CoT reasoning, their direct response accuracy can also be improved through implicit reasoning capabilities. To this end, this paper proposes UnifiedReward-Think, the first unified multimodal CoT-based reward model, capable of multi-dimensional, step-by-step long-chain reasoning for both visual understanding and generation reward tasks. Specifically, we adopt an exploration-driven reinforcement fine-tuning approach to elicit and incentivize the model's latent complex reasoning ability: (1) We first use a small amount of image generation preference data to distill the reasoning process of GPT-4o, which is then used for the model's cold start to learn the format and structure of CoT reasoning. (2) Subsequently, by leveraging the model's prior knowledge and generalization capabilities, we prepare large-scale unified multimodal preference data to elicit the model's reasoning process across various vision tasks. During this phase, correct reasoning outputs are retained for rejection sampling to refine the model (3) while incorrect predicted samples are finally used for Group Relative Policy Optimization (GRPO) based reinforcement fine-tuning, enabling the model to explore diverse reasoning paths and optimize for correct and robust solutions. Extensive experiments across various vision reward tasks demonstrate the superiority of our model.

Standard reinforcement learning from human feedback (RLHF) trains a reward model on pairwise preference data and then uses it for policy optimization. However, while reward models are optimized to capture relative preferences, existing policy optimization techniques rely on absolute reward magnitudes during training. In settings where the rewards are non-verifiable such as summarization, instruction following, and chat completion, this misalignment often leads to suboptimal performance. We introduce Group Ordinal Policy Optimization (GOPO), a policy optimization method that uses only the ranking of the rewards and discards their magnitudes. Our rank-based transformation of rewards provides several gains, compared to Group Relative Policy Optimization (GRPO), in settings with non-verifiable rewards: (1) consistently higher training/validation reward trajectories, (2) improved LLM-as-judge evaluations across most intermediate training steps, and (3) reaching a policy of comparable quality in substantially less training steps than GRPO. We demonstrate consistent improvements across a range of tasks and model sizes.

In this paper, we aim to tackle the limitation of the Adversarial Inverse Reinforcement Learning (AIRL) method in stochastic environments where theoretical results cannot hold and performance is degraded. To address this issue, we propose a novel method which infuses the dynamics information into the reward shaping with the theoretical guarantee for the induced optimal policy in the stochastic environments. Incorporating our novel model-enhanced rewards, we present a novel Model-Enhanced AIRL framework, which integrates transition model estimation directly into reward shaping. Furthermore, we provide a comprehensive theoretical analysis of the reward error bound and performance difference bound for our method. The experimental results in MuJoCo benchmarks show that our method can achieve superior performance in stochastic environments and competitive performance in deterministic environments, with significant improvement in sample efficiency, compared to existing baselines.

Exploration remains a critical challenge in online reinforcement learning, as an agent must effectively explore unknown environments to achieve high returns. Currently, the main exploration algorithms are primarily count-based methods and curiosity-based methods, with prediction-error methods being a prominent example. In this paper, we propose a novel method called Random Distribution Distillation (RDD), which samples the output of a target network from a normal distribution. RDD facilitates a more extensive exploration by explicitly treating the difference between the prediction network and the target network as an intrinsic reward. Furthermore, by introducing randomness into the output of the target network for a given state and modeling it as a sample from a normal distribution, intrinsic rewards are bounded by two key components: a pseudo-count term ensuring proper exploration decay and a discrepancy term accounting for predictor convergence. We demonstrate that RDD effectively unifies both count-based and prediction-error approaches. It retains the advantages of prediction-error methods in high-dimensional spaces, while also implementing an intrinsic reward decay mode akin to the pseudo-count method. In the experimental section, RDD is compared with more advanced methods in a series of environments. Both theoretical analysis and experimental results confirm the effectiveness of our approach in improving online exploration for reinforcement learning tasks.

In Reinforcement Learning (RL), Laplacian Representation (LapRep) is a task-agnostic state representation that encodes the geometry of the environment. A desirable property of LapRep stated in prior works is that the Euclidean distance in the LapRep space roughly reflects the reachability between states, which motivates the usage of this distance for reward shaping. However, we find that LapRep does not necessarily have this property in general: two states having small distance under LapRep can actually be far away in the environment. Such mismatch would impede the learning process in reward shaping. To fix this issue, we introduce a Reachability-Aware Laplacian Representation (RA-LapRep), by properly scaling each dimension of LapRep. Despite the simplicity, we demonstrate that RA-LapRep can better capture the inter-state reachability as compared to LapRep, through both theoretical explanations and experimental results. Additionally, we show that this improvement yields a significant boost in reward shaping performance and also benefits bottleneck state discovery.