Daily Papers

Group-based reinforcement learning (RL), such as GRPO, has advanced the capabilities of large language models on long-horizon agentic tasks. To enable more fine-grained policy updates, recent research has increasingly shifted toward stepwise group-based policy optimization, which treats each step in a rollout trajectory independently while using a memory module to retain historical context. However, we find a key issue in estimating stepwise relative advantages, namely context inconsistency, where steps within the same group may differ in their historical contexts. Empirically, we reveal that this issue can lead to severely biased advantage estimation, thereby degrading policy optimization significantly. To address the issue, in this paper, we propose Hierarchy-of-Groups Policy Optimization (HGPO) for long-horizon agentic tasks. Specifically, within a group of rollout trajectories, HGPO assigns each step to multiple hierarchical groups according to the consistency of historical contexts. Then, for each step, HGPO computes distinct advantages within each group and aggregates them with an adaptive weighting scheme. In this way, HGPO can achieve a favorable bias-variance trade-off in stepwise advantage estimation, without extra models or rollouts. Evaluations on two challenging agentic tasks, ALFWorld and WebShop with Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct, show that HGPO significantly outperforms existing agentic RL methods under the same computational constraints. Code is available at https://github.com/langfengQ/verl-agent/tree/master/recipe/hgpo.

The VAPO framework has demonstrated significant empirical success in enhancing the efficiency and reliability of reinforcement learning for long chain-of-thought (CoT) reasoning tasks with large language models (LLMs). By systematically addressing challenges such as value model bias, heterogeneous sequence lengths, and sparse reward signals, VAPO achieves state-of-the-art performance. While its practical benefits are evident, a deeper theoretical understanding of its underlying mechanisms and potential limitations is crucial for guiding future advancements. This paper aims to initiate such a discussion by exploring VAPO from a theoretical perspective, highlighting areas where its assumptions might be challenged and where further investigation could yield more robust and generalizable reasoning agents. We delve into the intricacies of value function approximation in complex reasoning spaces, the optimality of adaptive advantage estimation, the impact of token-level optimization, and the enduring challenges of exploration and generalization.

Reinforcement learning (RL) is widely used for post-training large language models (LLMs) in code editing, where group-relative methods, such as GRPO, are popular due to their critic-free and normalized advantage estimation. However, in real-world code-editing scenarios, reward distributions are often skewed with unpredictable noise, leading to distorted advantage computation and increased rollout outliers. To address this issue, we propose Group Adaptive Policy Optimization (GAPO), which adaptively finds an interval with the highest SNR (Signal to Noise Ratio) per prompt and uses the median of that interval as an adaptive Q to replace the group mean in advantage calculation to reduce noise further. This adaptive Q robustly handles rollout noise while remaining plug-and-play and efficient. We evaluate GAPO on nine instruction-tuned LLMs (3B-14B) using a collected large dataset of 51,844 real-world, history-aware code-editing tasks spanning 10 programming languages. GAPO yields up to 4.35 in-domain (ID) and 5.30 out-of-domain (OOD) exact-match improvements over GRPO and its variant DAPO, while achieving lower clipping ratios and higher GPU throughput. Code: https://github.com/TsingZ0/verl-GAPO.

To combine the advantages of Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), recent methods have integrated ''hints'' into post-training, which are prefix segments of complete reasoning trajectories, aiming for powerful knowledge expansion and reasoning generalization. However, existing hint-based RL methods typically ignore difficulty when scheduling hint ratios and estimating relative advantages, leading to unstable learning and excessive imitation of off-policy hints. In this work, we propose ADHint, which treats difficulty as a key factor in both hint-ratio schedule and relative-advantage estimation to achieve a better trade-off between exploration and imitation. Specifically, we propose Adaptive Hint with Sample Difficulty Prior, which evaluates each sample's difficulty under the policy model and accordingly schedules an appropriate hint ratio to guide its rollouts. We also introduce Consistency-based Gradient Modulation and Selective Masking for Hint Preservation to modulate token-level gradients within hints, preventing biased and destructive updates. Additionally, we propose Advantage Estimation with Rollout Difficulty Posterior, which leverages the relative difficulty of rollouts with and without hints to estimate their respective advantages, thereby achieving more balanced updates. Extensive experiments across diverse modalities, model scales, and domains demonstrate that ADHint delivers superior reasoning ability and out-of-distribution generalization, consistently surpassing existing methods in both pass@1 and avg@8. Our code and dataset will be made publicly available upon paper acceptance.

Reinforcement Learning from Verifier Rewards (RLVR) has emerged as a widely used approach for post-training large language models on reasoning tasks, with group-based methods such as GRPO and its variants gaining broad adoption. These methods rely on group-relative advantage estimation to avoid learned critics, yet its theoretical properties remain poorly understood. In this work, we uncover a fundamental issue of group-based RL: the group-relative advantage estimator is inherently biased relative to the true (expected) advantage. We provide the first theoretical analysis showing that it systematically underestimates advantages for hard prompts and overestimates them for easy prompts, leading to imbalanced exploration and exploitation. To address this issue, we propose History-Aware Adaptive Difficulty Weighting (HA-DW), an adaptive reweighting scheme that adjusts advantage estimates based on an evolving difficulty anchor and training dynamics. Both theoretical analysis and experiments on five mathematical reasoning benchmarks demonstrate that HA-DW consistently improves performance when integrated into GRPO and its variants. Our results suggest that correcting biased advantage estimation is critical for robust and efficient RLVR training.

Vision-Language Models (VLMs) have achieved remarkable success in visual question answering tasks, but their reliance on large numbers of visual tokens introduces significant computational overhead. While existing efficient VLM approaches reduce visual tokens through fixed-ratio compression, they operate passively and lack the ability to adapt to varying task requirements. This motivates a fundamental question: Can VLMs autonomously determine the minimum number of visual tokens required for each sample? Inspired by human active vision mechanisms, we introduce AdaptVision, an efficient VLM paradigm that enables adaptive visual token acquisition through a coarse-to-fine approach. Our model initially processes compressed visual tokens from low-resolution images and selectively acquires additional visual information by invoking a bounding box tool to crop key regions when necessary. We train AdaptVision using a reinforcement learning framework that carefully balances accuracy and efficiency. Central to our approach is Decoupled Turn Policy Optimization (DTPO), which decouples the learning objective into two components: (1) tool learning, which optimizes correct tool utilization, and (2) accuracy improvement, which refines the generated responses to improve answer correctness. Based on this formulation, we further decouple advantage estimation by computing separate advantages for tokens associated with each objective. This formulation enables more effective optimization for AdaptVision compared to vanilla GRPO. Comprehensive experiments across multiple VQA benchmarks demonstrate that AdaptVision achieves superior performance while consuming substantially fewer visual tokens than state-of-the-art efficient VLM methods.

We introduce QwenLong-L1.5, a model that achieves superior long-context reasoning capabilities through systematic post-training innovations. The key technical breakthroughs of QwenLong-L1.5 are as follows: (1) Long-Context Data Synthesis Pipeline: We develop a systematic synthesis framework that generates challenging reasoning tasks requiring multi-hop grounding over globally distributed evidence. By deconstructing documents into atomic facts and their underlying relationships, and then programmatically composing verifiable reasoning questions, our approach creates high-quality training data at scale, moving substantially beyond simple retrieval tasks to enable genuine long-range reasoning capabilities. (2) Stabilized Reinforcement Learning for Long-Context Training: To overcome the critical instability in long-context RL, we introduce task-balanced sampling with task-specific advantage estimation to mitigate reward bias, and propose Adaptive Entropy-Controlled Policy Optimization (AEPO) that dynamically regulates exploration-exploitation trade-offs. (3) Memory-Augmented Architecture for Ultra-Long Contexts: Recognizing that even extended context windows cannot accommodate arbitrarily long sequences, we develop a memory management framework with multi-stage fusion RL training that seamlessly integrates single-pass reasoning with iterative memory-based processing for tasks exceeding 4M tokens. Based on Qwen3-30B-A3B-Thinking, QwenLong-L1.5 achieves performance comparable to GPT-5 and Gemini-2.5-Pro on long-context reasoning benchmarks, surpassing its baseline by 9.90 points on average. On ultra-long tasks (1M~4M tokens), QwenLong-L1.5's memory-agent framework yields a 9.48-point gain over the agent baseline. Additionally, the acquired long-context reasoning ability translates to enhanced performance in general domains like scientific reasoning, memory tool using, and extended dialogue.

We present Aryabhata 1.0, a compact 7B parameter math reasoning model optimized for the Indian academic exam, the Joint Entrance Examination (JEE). Despite rapid progress in large language models (LLMs), current models often remain unsuitable for educational use. Aryabhata 1.0 is built by merging strong open-weight reasoning models, followed by supervised fine-tuning (SFT) with curriculum learning on verified chain-of-thought (CoT) traces curated through best-of-n rejection sampling. To further boost performance, we apply reinforcement learning with verifiable rewards (RLVR) using A2C objective with group-relative advantage estimation alongwith novel exploration strategies such as Adaptive Group Resizing and Temperature Scaling. Evaluated on both in-distribution (JEE Main 2025) and out-of-distribution (MATH, GSM8K) benchmarks, Aryabhata outperforms existing models in accuracy and efficiency, while offering pedagogically useful step-by-step reasoning. We release Aryabhata as a foundation model to advance exam-centric, open-source small language models. This marks our first open release for community feedback (https://huggingface.co/PhysicsWallahAI/Aryabhata-1.0{Aryabhata 1.0 on Hugging Face}); PW is actively training future models to further improve learning outcomes for students.

Large Language Model (LLM) Agents exhibit inherent reasoning abilities through the collaboration of multiple tools. However, during agent inference, existing methods often suffer from (i) locally myopic generation, due to the absence of lookahead, and (ii) trajectory instability, where minor early errors can escalate into divergent reasoning paths. These issues make it difficult to balance global effectiveness and computational efficiency. To address these two issues, we propose meta-adaptive exploration with LLM agents https://github.com/exoskeletonzj/MAXS, a meta-adaptive reasoning framework based on LLM Agents that flexibly integrates tool execution and reasoning planning. MAXS employs a lookahead strategy to extend reasoning paths a few steps ahead, estimating the advantage value of tool usage, and combines step consistency variance and inter-step trend slopes to jointly select stable, consistent, and high-value reasoning steps. Additionally, we introduce a trajectory convergence mechanism that controls computational cost by halting further rollouts once path consistency is achieved, enabling a balance between resource efficiency and global effectiveness in multi-tool reasoning. We conduct extensive empirical studies across three base models (MiMo-VL-7B, Qwen2.5-VL-7B, Qwen2.5-VL-32B) and five datasets, demonstrating that MAXS consistently outperforms existing methods in both performance and inference efficiency. Further analysis confirms the effectiveness of our lookahead strategy and tool usage.

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

In Reinforcement Learning with Verifiable Rewards (RLVR), constructing a robust advantage baseline is critical for policy gradients, effectively guiding the policy model to reinforce desired behaviors. Recent research has introduced Generalist Value Models (such as V_0), which achieve pre-trained value estimation by explicitly encoding model capabilities in-context, eliminating the need to synchronously update the value model alongside the policy model. In this paper, we propose V_{0.5}, which adaptively fuses the baseline predicted by such value model (acting as a prior) with the empirical mean derived from sparse rollouts. This constructs a robust baseline that balances computational efficiency with extremely low variance. Specifically, we introduce a real-time statistical testing and dynamic budget allocation. This balances the high variance caused by sparse sampling against the systematic bias (or hallucinations) inherent in the value model's prior. By constructing a hypothesis test to evaluate the prior's reliability in real-time, the system dynamically allocates additional rollout budget on demand. This mechanism minimizes the baseline estimator's Mean Squared Error (MSE), guaranteeing stable policy gradients, even under extreme sparsity with a group size of 4. Extensive evaluations across six mathematical reasoning benchmarks demonstrate that V_{0.5} significantly outperforms GRPO and DAPO, achieving faster convergence and over some 10% performance improvement.

Reinforcement learning has become a cornerstone technique for developing reasoning models in complex tasks, ranging from mathematical problem-solving to imaginary reasoning. The optimization of these models typically relies on policy gradient methods, whose efficacy hinges on the accurate estimation of an advantage function. However, prevailing methods typically employ static advantage estimation, a practice that leads to inefficient credit assignment by neglecting the dynamic utility of training samples over time. This limitation results in suboptimal policy updates, which in turn manifest as slower convergence rates and increased learning instability, as models fail to adapt to evolving sample utilities effectively. To address this problem, we introduce ADORA (Advantage Dynamics via Online Rollout Adaptation), a novel framework for policy optimization. ADORA dynamically adjusts the advantage function's weighting by adaptively categorizing training data into temporarily advantageous and disadvantageous samples, based on their evolving utility during online model rollouts. This tailored data differentiation strategy allows ADORA to be seamlessly integrated into existing policy optimization algorithms without significant architectural modifications, enabling the policy to prioritize learning from more informative experiences and thereby achieve more efficient policy updates. Extensive evaluations across diverse model families and varying data scales demonstrate that ADORA is a robust and efficient framework. It significantly enhances long reasoning in both geometric and mathematical tasks, consistently achieving notable performance gains without requiring sensitive hyperparameter tuning.

Learning from off-policy data is essential for sample-efficient reinforcement learning. In the present work, we build on the insight that the advantage function can be understood as the causal effect of an action on the return, and show that this allows us to decompose the return of a trajectory into parts caused by the agent's actions (skill) and parts outside of the agent's control (luck). Furthermore, this decomposition enables us to naturally extend Direct Advantage Estimation (DAE) to off-policy settings (Off-policy DAE). The resulting method can learn from off-policy trajectories without relying on importance sampling techniques or truncating off-policy actions. We draw connections between Off-policy DAE and previous methods to demonstrate how it can speed up learning and when the proposed off-policy corrections are important. Finally, we use the MinAtar environments to illustrate how ignoring off-policy corrections can lead to suboptimal policy optimization performance.

Recent advances in reinforcement learning for foundation models, such as Group Relative Policy Optimization (GRPO), have significantly improved the performance of foundation models on reasoning tasks. Notably, the advantage function serves as a central mechanism in GRPO for ranking the trajectory importance. However, existing explorations encounter both advantage reversion and advantage mirror problems, which hinder the reasonable advantage allocation across different query samples. In this work, we propose an easy but effective GRPO strategy, Mixed Advantage Policy Optimization (MAPO). We reveal that the trajectory appears with different certainty and propose the advantage percent deviation for samples with high-certainty trajectories. Furthermore, we dynamically reweight the advantage function for samples with varying trajectory certainty, thereby adaptively configuring the advantage function to account for sample-specific characteristics. Comparison with related state-of-the-art methods, along with ablation studies on different advantage variants, validates the effectiveness of our approach.

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates for estimating more efficiently multiple expectations with the same sample. We first show that there exists a family of optimal estimators combining both importance sampling and control variates, which however cannot be used in practice because they require the knowledge of the values of the expectations to estimate. Motivated by the form of these optimal estimators and some interesting properties, we therefore propose an adaptive algorithm. The general idea is to adaptively update the parameters of the estimators for approaching the optimal ones. We suggest then a quantitative stopping criterion that exploits the trade-off between approaching these optimal parameters and having a sufficient budget left. This left budget is then used to draw a new independent sample from the final sampling distribution, allowing to get unbiased estimators of the expectations. We show how to apply our procedure to sensitivity analysis, by estimating Sobol' indices and quantifying the impact of the input distributions. Finally, realistic test cases show the practical interest of the proposed algorithm, and its significant improvement over estimating the expectations separately.

Reinforcement learning (RL) has emerged as an effective approach for enhancing the reasoning capabilities of large language models (LLMs), especially in scenarios where supervised fine-tuning (SFT) falls short due to limited chain-of-thought (CoT) data. Among RL-based post-training methods, group relative advantage estimation, as exemplified by Group Relative Policy Optimization (GRPO), has attracted considerable attention for eliminating the dependency on the value model, thereby simplifying training compared to traditional approaches like Proximal Policy Optimization (PPO). However, we observe that exsiting group relative advantage estimation method still suffers from training inefficiencies, particularly when the estimated advantage approaches zero. To address this limitation, we propose Advantage-Augmented Policy Optimization (AAPO), a novel RL algorithm that optimizes the cross-entropy (CE) loss using advantages enhanced through a momentum-based estimation scheme. This approach effectively mitigates the inefficiencies associated with group relative advantage estimation. Experimental results on multiple mathematical reasoning benchmarks demonstrate the superior performance of AAPO.

Group Relative Policy Optimization (GRPO) assigns a single scalar advantage to all tokens in a completion. For structured generations with explicit segments and objectives, this couples unrelated reward signals across segments, leading to objective interference and misattributed credit. We propose Blockwise Advantage Estimation, a family of GRPO-compatible methods that assigns each objective its own advantage and applies it only to the tokens in the corresponding text block, reducing reliance on hand-designed scalar rewards and scaling naturally to additional objectives. A key challenge is estimating advantages for later blocks whose rewards are conditioned on sampled prefixes; standard unbiased approaches require expensive nested rollouts from intermediate states. Concretely, we introduce an Outcome-Conditioned Baseline that approximates intermediate state values using only within-group statistics by stratifying samples according to a prefix-derived intermediate outcome. On math tasks with uncertainty estimation, our method mitigates reward interference, is competitive with a state-of-the-art reward-designed approach, and preserves test-time gains from confidence-weighted ensembling. More broadly, it provides a modular recipe for optimizing sequential objectives in structured generations without additional rollouts.

This study addresses the challenge of estimating average treatment effects (ATEs) for advertising campaigns in online marketplaces where complete randomized experimentation is infeasible. We propose two key innovations: (1) a shrinkage estimator that optimally combines observational and experimental data without assuming smooth treatment effects across campaigns, and (2) a Bayesian adaptive experimental design framework that efficiently selects campaigns for randomized evaluation that minimizes cumulative risk. Our shrinkage estimator achieves lower risk compared to existing methods by balancing bias-variance tradeoffs, while our adaptive design significantly reduces the costs of campaign randomization. We establish theoretical guarantees including asymptotic normality and regret bounds. In an application to Amazon Ads data analyzing 2,583 campaigns, our approach achieves equivalent estimation precision while requiring only half of the randomized experiments needed by random sampling, the standard method widely used in practice today. The proposed method serves as a practical solution for marketplace platforms to efficiently measure advertising effectiveness while managing experimentation costs.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

We theoretically explore the relationship between sample-efficiency and adaptivity in reinforcement learning. An algorithm is sample-efficient if it uses a number of queries n to the environment that is polynomial in the dimension d of the problem. Adaptivity refers to the frequency at which queries are sent and feedback is processed to update the querying strategy. To investigate this interplay, we employ a learning framework that allows sending queries in K batches, with feedback being processed and queries updated after each batch. This model encompasses the whole adaptivity spectrum, ranging from non-adaptive 'offline' (K=1) to fully adaptive (K=n) scenarios, and regimes in between. For the problems of policy evaluation and best-policy identification under d-dimensional linear function approximation, we establish Omega(log log d) lower bounds on the number of batches K required for sample-efficient algorithms with n = O(poly(d)) queries. Our results show that just having adaptivity (K>1) does not necessarily guarantee sample-efficiency. Notably, the adaptivity-boundary for sample-efficiency is not between offline reinforcement learning (K=1), where sample-efficiency was known to not be possible, and adaptive settings. Instead, the boundary lies between different regimes of adaptivity and depends on the problem dimension.

Reinforcement Learning has emerged as the fundamental technique for enhancing reasoning in LLMs. However, existing algorithms apply uniform optimization to all tokens, ignoring their different roles in reasoning process. To address this limitation, we introduce Heterogeneous Adaptive Policy Optimization (HAPO), a comprehensive token-aware algorithm that dynamically adapts optimization based on token entropy. For rollout sampling, we propose Adaptive Temperature Sampling, which adjusts sampling temperature in real time, promoting exploration at high-entropy tokens while preserving coherence at low-entropy ones. For advantage calculation, we introduce Token Level Group Average that normalizes advantages at token level, jointly accounting for sequence-length as in token-mean loss while preserving non-biased treatment. We then develop Differential Advantage Redistribution that leverages entropy and importance ratios to modulate rewards-adjusting updates for tokens with clear signals. For clipping loss, we design Asymmetric Adaptive Clipping, allowing aggressive probability reduction for noisy low-entropy tokens while enabling exploration for high-entropy tokens. Through systematic investigation between entropy and training dynamics, we embedded token-level treatment into every stages to achieve fine-grained control. Extensive experiments demonstrate that HAPO consistently outperforms DAPO across multiple model scales. Our code can be found in https://github.com/starriver030515/HAPO.

We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner's prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano's inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

Fast changing states or volatile environments pose a significant challenge to online optimization, which needs to perform rapid adaptation under limited observation. In this paper, we give query and regret optimal bandit algorithms under the strict notion of strongly adaptive regret, which measures the maximum regret over any contiguous interval I. Due to its worst-case nature, there is an almost-linear Omega(|I|^{1-epsilon}) regret lower bound, when only one query per round is allowed [Daniely el al, ICML 2015]. Surprisingly, with just two queries per round, we give Strongly Adaptive Bandit Learner (StABL) that achieves O(n|I|) adaptive regret for multi-armed bandits with n arms. The bound is tight and cannot be improved in general. Our algorithm leverages a multiplicative update scheme of varying stepsizes and a carefully chosen observation distribution to control the variance. Furthermore, we extend our results and provide optimal algorithms in the bandit convex optimization setting. Finally, we empirically demonstrate the superior performance of our algorithms under volatile environments and for downstream tasks, such as algorithm selection for hyperparameter optimization.

Humans have the ability to adapt the type of information they use, the procedure they employ, and the amount of time they spend when solving problems. However, most standard neural networks have a fixed function type and computation budget regardless of the sample's nature or difficulty. Adaptivity is a powerful paradigm as it not only imbues practitioners with flexibility pertaining to the downstream usage of these models but can also serve as a powerful inductive bias for solving certain challenging classes of problems. In this work, we introduce a new approach called AdaTape, which allows for dynamic computation in neural networks through adaptive tape tokens. AdaTape utilizes an elastic input sequence by equipping an architecture with a dynamic read-and-write tape. Specifically, we adaptively generate input sequences using tape tokens obtained from a tape bank which can be either trainable or derived from input data. We examine the challenges and requirements to obtain dynamic sequence content and length, and propose the Adaptive Tape Reading (ATR) algorithm to achieve both goals. Through extensive experiments on image recognition tasks, we show that AdaTape can achieve better performance while maintaining the computational cost. To facilitate further research, we have released code at https://github.com/google-research/scenic.

Indirect experiments provide a valuable framework for estimating treatment effects in situations where conducting randomized control trials (RCTs) is impractical or unethical. Unlike RCTs, indirect experiments estimate treatment effects by leveraging (conditional) instrumental variables, enabling estimation through encouragement and recommendation rather than strict treatment assignment. However, the sample efficiency of such estimators depends not only on the inherent variability in outcomes but also on the varying compliance levels of users with the instrumental variables and the choice of estimator being used, especially when dealing with numerous instrumental variables. While adaptive experiment design has a rich literature for direct experiments, in this paper we take the initial steps towards enhancing sample efficiency for indirect experiments by adaptively designing a data collection policy over instrumental variables. Our main contribution is a practical computational procedure that utilizes influence functions to search for an optimal data collection policy, minimizing the mean-squared error of the desired (non-linear) estimator. Through experiments conducted in various domains inspired by real-world applications, we showcase how our method can significantly improve the sample efficiency of indirect experiments.

We introduce ADEPT: Adaptive Data ExPloiTation, a simple yet powerful framework to enhance the **data efficiency** and **generalization** in deep reinforcement learning (RL). Specifically, ADEPT adaptively manages the use of sampled data across different learning stages via multi-armed bandit (MAB) algorithms, optimizing data utilization while mitigating overfitting. Moreover, ADEPT can significantly reduce the computational overhead and accelerate a wide range of RL algorithms. We test ADEPT on benchmarks including Procgen, MiniGrid, and PyBullet. Extensive simulation demonstrates that ADEPT can achieve superior performance with remarkable computational efficiency, offering a practical solution to data-efficient RL. Our code is available at https://github.com/yuanmingqi/ADEPT.

Traditional direct estimation methods are not efficient for domains of a survey population with small sample sizes. To estimate the domain proportions, we combine the direct estimators and the regression-synthetic estimators based on domain-level auxiliary information. For the case of small true proportions, we introduce the design-based linear combination that is a robust alternative to the empirical best linear unbiased predictor (EBLUP) based on the Fay--Herriot model. We also consider an adaptive procedure optimizing a sample-size-dependent composite estimator, which depends on a single parameter for all domains. We imitate the Lithuanian Labor Force Survey, where we estimate the proportions of the unemployed and employed in municipalities. We show where the considered design-based compositions and estimators of their mean square errors are competitive for EBLUP and its accuracy estimation.

Reinforcement Learning with Verifiable Rewards (RLVR) for large language models (LLMs) has achieved remarkable progress in enhancing LLMs' reasoning capabilities on tasks with clear correctness criteria, such as mathematical reasoning tasks. Several training metrics, such as entropy or response length, have been observed to correlate with different reasoning behaviors in reinforcement learning. Prior approaches incorporate such priors through reward or advantage shaping, which often relies on hand-crafted penalties and preferences (e.g., higher-is-better or lower-is-better). However, without careful hyperparameter tuning, these directional priors can be overly biased and may lead to failure. To this end, we introduce Conditional advANtage estimatiON (CANON), amplifying the impact of the target metric without presuming its direction. Specifically, CANON regroups the sampled responses into two groups based on the higher or lower value of a target metric, measures which metric trend contributes to better performance through inter-group comparison, and identifies the better response within the same group. In summary, CANON based on entropy consistently outperforms prior methods across three LLMs on both math reasoning and high-complexity logic tasks. When applied to response length, CANON further improves token efficiency, yielding a more favorable Pareto frontier in the performance-cost trade-off.

In this work, we investigate how explicitly modeling problem's difficulty prior information shapes the effectiveness of reinforcement learning based fine-tuning for multimodal reasoning. Our exploration mainly comprises of following three perspective: First, through offline data curation, we analyze the U-shaped difficulty distribution of two given datasets using the base model by multi-round sampling, and then filter out prompts that are either too simple or extremely difficult to provide meaningful gradients and perform subsequent two-stage training. Second, we implement an online advantage differentiation, computing group-wise empirical accuracy as a difficulty proxy to adaptively reweight advantages estimation, providing stronger learning signals for more challenging problems. Finally, we introduce difficulty hints as explicit prompts for more complex samples in the second training stage, encouraging the model to calibrate its reasoning depth and perform reflective validation checks. Our comprehensive approach demonstrates significant performances across various multi-modal mathematical reasoning benchmarks with only 2K+0.6K two-stage training data.

Training LLMs as interactive agents for multi-turn decision-making remains challenging, particularly in long-horizon tasks with sparse and delayed rewards, where agents must execute extended sequences of actions before receiving meaningful feedback. Most existing reinforcement learning (RL) approaches model LLM agents as flat policies operating at a single time scale, selecting one action at each turn. In sparse-reward settings, such flat policies must propagate credit across the entire trajectory without explicit temporal abstraction, which often leads to unstable optimization and inefficient credit assignment. We propose HiPER, a novel Hierarchical Plan-Execute RL framework that explicitly separates high-level planning from low-level execution. HiPER factorizes the policy into a high-level planner that proposes subgoals and a low-level executor that carries them out over multiple action steps. To align optimization with this structure, we introduce a key technique called hierarchical advantage estimation (HAE), which carefully assigns credit at both the planning and execution levels. By aggregating returns over the execution of each subgoal and coordinating updates across the two levels, HAE provides an unbiased gradient estimator and provably reduces variance compared to flat generalized advantage estimation. Empirically, HiPER achieves state-of-the-art performance on challenging interactive benchmarks, reaching 97.4\% success on ALFWorld and 83.3\% on WebShop with Qwen2.5-7B-Instruct (+6.6\% and +8.3\% over the best prior method), with especially large gains on long-horizon tasks requiring multiple dependent subtasks. These results highlight the importance of explicit hierarchical decomposition for scalable RL training of multi-turn LLM agents.

Modern preference alignment techniques, such as Best-of-N (BoN) sampling, rely on reward models trained with pairwise comparison data. While effective at learning relative preferences, this paradigm fails to capture a signal of response acceptability, leaving systems vulnerable to selecting the least bad of many unacceptable options. This is particularly problematic for hard prompts, where the risk of such false acceptances increases with the number of samples. In this paper, we address this critical reliability gap by introducing a new data collection and modeling framework. By augmenting preference data with an outside option, inspired by discrete choice models, we train a reward model that can distinguish not just what is better, but what is good enough. We leverage this capability to create an adaptive inference strategy, best of mini-N in-loop, which partitions the generation budget into sequential loops with a calibrated, early-exit condition. Our experiments show that when tuned as an alignment guardrail, it reduces reliability failures by 70\%, and when tuned as an inference accelerator, it improves average inference speed by over 22\% in IMDB-sentiment setting. We thus provide a principled and flexible framework for practitioners to explicitly manage the trade-off between reliability and computational efficiency.

Reinforcement learning has emerged as a paradigm for post-training large language models, boosting their reasoning capabilities. Such approaches compute an advantage value for each sample, reflecting better or worse performance than expected, thereby yielding both positive and negative signals for training. However, the indiscriminate mixing of the two signals in existing methods, especially from the early stages, may lead to ambiguous guidance and limited gains. To address this issue, we propose **CAPO** (**C**urriculum **A**dvantage **P**olicy **O**ptimization), an adaptive curriculum mechanism based on advantage signals. The proposed mechanism bootstraps imitation learning with positive-only advantage samples to establish robust foundations, and subsequently introduces negative signals to cultivate discriminative capabilities, thereby improving generalization across complex scenarios. Compatible with diverse optimization methods including GRPO, PPO, RLOO, and Reinforce++, our method consistently achieves stable and significant improvements in mathematical reasoning tasks, and further generalizes effectively to multimodal Graphical User Interface (GUI) reasoning scenarios, establishing itself as a versatile and robust optimization framework.

In offline reinforcement learning, the challenge of out-of-distribution (OOD) is pronounced. To address this, existing methods often constrain the learned policy through policy regularization. However, these methods often suffer from the issue of unnecessary conservativeness, hampering policy improvement. This occurs due to the indiscriminate use of all actions from the behavior policy that generates the offline dataset as constraints. The problem becomes particularly noticeable when the quality of the dataset is suboptimal. Thus, we propose Adaptive Advantage-guided Policy Regularization (A2PR), obtaining high-advantage actions from an augmented behavior policy combined with VAE to guide the learned policy. A2PR can select high-advantage actions that differ from those present in the dataset, while still effectively maintaining conservatism from OOD actions. This is achieved by harnessing the VAE capacity to generate samples matching the distribution of the data points. We theoretically prove that the improvement of the behavior policy is guaranteed. Besides, it effectively mitigates value overestimation with a bounded performance gap. Empirically, we conduct a series of experiments on the D4RL benchmark, where A2PR demonstrates state-of-the-art performance. Furthermore, experimental results on additional suboptimal mixed datasets reveal that A2PR exhibits superior performance. Code is available at https://github.com/ltlhuuu/A2PR.

Enhancing the reasoning capabilities of large language models effectively using reinforcement learning (RL) remains a crucial challenge. Existing approaches primarily adopt two contrasting advantage estimation granularities: Token-level methods (e.g., PPO) aim to provide the fine-grained advantage signals but suffer from inaccurate estimation due to difficulties in training an accurate critic model. On the other extreme, trajectory-level methods (e.g., GRPO) solely rely on a coarse-grained advantage signal from the final reward, leading to imprecise credit assignment. To address these limitations, we propose Segment Policy Optimization (SPO), a novel RL framework that leverages segment-level advantage estimation at an intermediate granularity, achieving a better balance by offering more precise credit assignment than trajectory-level methods and requiring fewer estimation points than token-level methods, enabling accurate advantage estimation based on Monte Carlo (MC) without a critic model. SPO features three components with novel strategies: (1) flexible segment partition; (2) accurate segment advantage estimation; and (3) policy optimization using segment advantages, including a novel probability-mask strategy. We further instantiate SPO for two specific scenarios: (1) SPO-chain for short chain-of-thought (CoT), featuring novel cutpoint-based partition and chain-based advantage estimation, achieving 6-12 percentage point improvements in accuracy over PPO and GRPO on GSM8K. (2) SPO-tree for long CoT, featuring novel tree-based advantage estimation, which significantly reduces the cost of MC estimation, achieving 7-11 percentage point improvements over GRPO on MATH500 under 2K and 4K context evaluation. We make our code publicly available at https://github.com/AIFrameResearch/SPO.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

Label efficiency has become an increasingly important objective in deep learning applications. Active learning aims to reduce the number of labeled examples needed to train deep networks, but the empirical performance of active learning algorithms can vary dramatically across datasets and applications. It is difficult to know in advance which active learning strategy will perform well or best in a given application. To address this, we propose the first adaptive algorithm selection strategy for deep active learning. For any unlabeled dataset, our (meta) algorithm TAILOR (Thompson ActIve Learning algORithm selection) iteratively and adaptively chooses among a set of candidate active learning algorithms. TAILOR uses novel reward functions aimed at gathering class-balanced examples. Extensive experiments in multi-class and multi-label applications demonstrate TAILOR's effectiveness in achieving accuracy comparable or better than that of the best of the candidate algorithms. Our implementation of TAILOR is open-sourced at https://github.com/jifanz/TAILOR.

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size. The search direction contains gradient information preconditioned by a well-scaled diagonal preconditioning matrix that captures the local curvature information. Our methodology does not require the tedious task of learning rate tuning, as the learning rate is updated automatically without adding an extra hyperparameter. We provide convergence guarantees on a comprehensive collection of optimization problems, including convex, strongly convex, and nonconvex problems, in both deterministic and stochastic regimes. We also conduct an extensive empirical evaluation on standard machine learning problems, justifying our algorithm's versatility and demonstrating its strong performance compared to other start-of-the-art first-order and second-order methods.

There is a strong link between the general concept of intelligence and the ability to collect and use information. The theory of Bayes-adaptive exploration offers an attractive optimality framework for training machines to perform complex information gathering tasks. However, the computational complexity of the resulting optimal control problem has limited the diffusion of the theory to mainstream deep AI research. In this paper we exploit the inherent mathematical structure of Bayes-adaptive problems in order to dramatically simplify the problem by making the reward structure denser while simultaneously decoupling the learning of exploitation and exploration policies. The key to this simplification comes from the novel concept of cross-value (i.e. the value of being in an environment while acting optimally according to another), which we use to quantify the value of currently available information. This results in a new denser reward structure that "cashes in" all future rewards that can be predicted from the current information state. In a set of experiments we show that the approach makes it possible to learn challenging information gathering tasks without the use of shaping and heuristic bonuses in situations where the standard RL algorithms fail.

Recently, test-time scaling Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities across scientific and professional tasks by generating long chains-of-thought (CoT). As a crucial component for developing these reasoning models, reinforcement learning (RL), exemplified by Proximal Policy Optimization (PPO) and its variants, allows models to learn through trial and error. However, PPO can be time-consuming due to its inherent on-policy nature, which is further exacerbated by increasing response lengths. In this work, we propose Truncated Proximal Policy Optimization (T-PPO), a novel extension to PPO that improves training efficiency by streamlining policy update and length-restricted response generation. T-PPO mitigates the issue of low hardware utilization, an inherent drawback of fully synchronized long-generation procedures, where resources often sit idle during the waiting periods for complete rollouts. Our contributions are two-folds. First, we propose Extended Generalized Advantage Estimation (EGAE) for advantage estimation derived from incomplete responses while maintaining the integrity of policy learning. Second, we devise a computationally optimized mechanism that allows for the independent optimization of the policy and value models. By selectively filtering prompt and truncated tokens, this mechanism reduces redundant computations and accelerates the training process without sacrificing convergence performance. We demonstrate the effectiveness and efficacy of T-PPO on AIME 2024 with a 32B base model. The experimental results show that T-PPO improves the training efficiency of reasoning LLMs by up to 2.5x and outperforms its existing competitors.

Humans naturally adapt to diverse environments by learning underlying rules across worlds with different dynamics, observations, and reward structures. In contrast, existing agents typically demonstrate improvements via self-evolving within a single domain, implicitly assuming a fixed environment distribution. Cross-environment learning has remained largely unmeasured: there is no standard collection of controllable, heterogeneous environments, nor a unified way to represent how agents learn. We address these gaps in two steps. First, we propose AutoEnv, an automated framework that treats environments as factorizable distributions over transitions, observations, and rewards, enabling low-cost (4.12 USD on average) generation of heterogeneous worlds. Using AutoEnv, we construct AutoEnv-36, a dataset of 36 environments with 358 validated levels, on which seven language models achieve 12-49% normalized reward, demonstrating the challenge of AutoEnv-36. Second, we formalize agent learning as a component-centric process driven by three stages of Selection, Optimization, and Evaluation applied to an improvable agent component. Using this formulation, we design eight learning methods and evaluate them on AutoEnv-36. Empirically, the gain of any single learning method quickly decrease as the number of environments increases, revealing that fixed learning methods do not scale across heterogeneous environments. Environment-adaptive selection of learning methods substantially improves performance but exhibits diminishing returns as the method space expands. These results highlight both the necessity and the current limitations of agent learning for scalable cross-environment generalization, and position AutoEnv and AutoEnv-36 as a testbed for studying cross-environment agent learning. The code is avaiable at https://github.com/FoundationAgents/AutoEnv.

During language model decoding, it is known that using higher temperature sampling gives more creative responses, while lower temperatures are more factually accurate. However, such models are commonly applied to general instruction following, which involves both creative and fact seeking tasks, using a single fixed temperature across all examples and tokens. In this work, we introduce Adaptive Decoding, a layer added to the model to select the sampling temperature dynamically at inference time, at either the token or example level, in order to optimize performance. To learn its parameters we introduce Latent Preference Optimization (LPO) a general approach to train discrete latent variables such as choices of temperature. Our method outperforms all fixed decoding temperatures across a range of tasks that require different temperatures, including UltraFeedback, Creative Story Writing, and GSM8K.

Policy gradient methods rely on a baseline to measure the relative advantage of an action, ensuring the model reinforces behaviors that outperform its current average capability. In the training of Large Language Models (LLMs) using Actor-Critic methods (e.g., PPO), this baseline is typically estimated by a Value Model (Critic) often as large as the policy model itself. However, as the policy continuously evolves, the value model requires expensive, synchronous incremental training to accurately track the shifting capabilities of the policy. To avoid this overhead, Group Relative Policy Optimization (GRPO) eliminates the coupled value model by using the average reward of a group of rollouts as the baseline; yet, this approach necessitates extensive sampling to maintain estimation stability. In this paper, we propose V_0, a Generalist Value Model capable of estimating the expected performance of any model on unseen prompts without requiring parameter updates. We reframe value estimation by treating the policy's dynamic capability as an explicit context input; specifically, we leverage a history of instruction-performance pairs to dynamically profile the model, departing from the traditional paradigm that relies on parameter fitting to perceive capability shifts. Focusing on value estimation at State Zero (i.e., the initial prompt, hence V_0), our model serves as a critical resource scheduler. During GRPO training, V_0 predicts success rates prior to rollout, allowing for efficient sampling budget allocation; during deployment, it functions as a router, dispatching instructions to the most cost-effective and suitable model. Empirical results demonstrate that V_0 significantly outperforms heuristic budget allocation and achieves a Pareto-optimal trade-off between performance and cost in LLM routing tasks.

In this work, a simple and effective robust adaptive beamforming technique is proposed for uniform linear arrays, which is based on the power spectral estimation and uncertainty region (PSEUR) of the interference plus noise (IPN) components. In particular, two algorithms are presented to find the angular sector of interference in every snapshot based on the adopted spatial uncertainty region of the interference direction. Moreover, a power spectrum is introduced based on the estimation of the power of interference and noise components, which allows the development of a robust approach to IPN covariance matrix reconstruction. The proposed method has two main advantages. First, an angular region that contains the interference direction is updated based on the statistics of the array data. Secondly, the proposed IPN-PSEUR method avoids estimating the power spectrum of the whole range of possible directions of the interference sector. Simulation results show that the performance of the proposed IPN-PSEUR beamformer is almost always close to the optimal value across a wide range of signal-to-noise ratios.

Developing an agent capable of adapting to unseen environments remains a difficult challenge in imitation learning. This work presents Adaptive Return-conditioned Policy (ARP), an efficient framework designed to enhance the agent's generalization ability using natural language task descriptions and pre-trained multimodal encoders. Our key idea is to calculate a similarity between visual observations and natural language instructions in the pre-trained multimodal embedding space (such as CLIP) and use it as a reward signal. We then train a return-conditioned policy using expert demonstrations labeled with multimodal rewards. Because the multimodal rewards provide adaptive signals at each timestep, our ARP effectively mitigates the goal misgeneralization. This results in superior generalization performances even when faced with unseen text instructions, compared to existing text-conditioned policies. To improve the quality of rewards, we also introduce a fine-tuning method for pre-trained multimodal encoders, further enhancing the performance. Video demonstrations and source code are available on the project website: https://sites.google.com/view/2023arp.

Recent domain generalization (DG) approaches typically use the hypothesis learned on source domains for inference on the unseen target domain. However, such a hypothesis can be arbitrarily far from the optimal one for the target domain, induced by a gap termed ``adaptivity gap''. Without exploiting the domain information from the unseen test samples, adaptivity gap estimation and minimization are intractable, which hinders us to robustify a model to any unknown distribution. In this paper, we first establish a generalization bound that explicitly considers the adaptivity gap. Our bound motivates two strategies to reduce the gap: the first one is ensembling multiple classifiers to enrich the hypothesis space, then we propose effective gap estimation methods for guiding the selection of a better hypothesis for the target. The other method is minimizing the gap directly by adapting model parameters using online target samples. We thus propose Domain-specific Risk Minimization (DRM). During training, DRM models the distributions of different source domains separately; for inference, DRM performs online model steering using the source hypothesis for each arriving target sample. Extensive experiments demonstrate the effectiveness of the proposed DRM for domain generalization with the following advantages: 1) it significantly outperforms competitive baselines on different distributional shift settings; 2) it achieves either comparable or superior accuracies on all source domains compared to vanilla empirical risk minimization; 3) it remains simple and efficient during training, and 4) it is complementary to invariant learning approaches.

Training corpuses for vision language models (VLMs) typically lack sufficient amounts of decision-centric data. This renders off-the-shelf VLMs sub-optimal for decision-making tasks such as in-the-wild device control through graphical user interfaces (GUIs). While training with static demonstrations has shown some promise, we show that such methods fall short for controlling real GUIs due to their failure to deal with real-world stochasticity and non-stationarity not captured in static observational data. This paper introduces a novel autonomous RL approach, called DigiRL, for training in-the-wild device control agents through fine-tuning a pre-trained VLM in two stages: offline RL to initialize the model, followed by offline-to-online RL. To do this, we build a scalable and parallelizable Android learning environment equipped with a VLM-based evaluator and develop a simple yet effective RL approach for learning in this domain. Our approach runs advantage-weighted RL with advantage estimators enhanced to account for stochasticity along with an automatic curriculum for deriving maximal learning signal. We demonstrate the effectiveness of DigiRL using the Android-in-the-Wild (AitW) dataset, where our 1.3B VLM trained with RL achieves a 49.5% absolute improvement -- from 17.7 to 67.2% success rate -- over supervised fine-tuning with static human demonstration data. These results significantly surpass not only the prior best agents, including AppAgent with GPT-4V (8.3% success rate) and the 17B CogAgent trained with AitW data (38.5%), but also the prior best autonomous RL approach based on filtered behavior cloning (57.8%), thereby establishing a new state-of-the-art for digital agents for in-the-wild device control.

We address the problem of optimizing a Brownian motion. We consider a (random) realization W of a Brownian motion with input space in [0,1]. Given W, our goal is to return an ε-approximation of its maximum using the smallest possible number of function evaluations, the sample complexity of the algorithm. We provide an algorithm with sample complexity of order log^2(1/ε). This improves over previous results of Al-Mharmah and Calvin (1996) and Calvin et al. (2017) which provided only polynomial rates. Our algorithm is adaptive---each query depends on previous values---and is an instance of the optimism-in-the-face-of-uncertainty principle.

We consider online learning problems in the realizable setting, where there is a zero-loss solution, and propose new Differentially Private (DP) algorithms that obtain near-optimal regret bounds. For the problem of online prediction from experts, we design new algorithms that obtain near-optimal regret {O} big( varepsilon^{-1} log^{1.5}{d} big) where d is the number of experts. This significantly improves over the best existing regret bounds for the DP non-realizable setting which are {O} big( varepsilon^{-1} minbig{d, T^{1/3}log dbig} big). We also develop an adaptive algorithm for the small-loss setting with regret O(L^starlog d + varepsilon^{-1} log^{1.5}{d}) where L^star is the total loss of the best expert. Additionally, we consider DP online convex optimization in the realizable setting and propose an algorithm with near-optimal regret O big(varepsilon^{-1} d^{1.5} big), as well as an algorithm for the smooth case with regret O big( varepsilon^{-2/3} (dT)^{1/3} big), both significantly improving over existing bounds in the non-realizable regime.

Sampling is ubiquitous in machine learning methodologies. Due to the growth of large datasets and model complexity, we want to learn and adapt the sampling process while training a representation. Towards achieving this grand goal, a variety of sampling techniques have been proposed. However, most of them either use a fixed sampling scheme or adjust the sampling scheme based on simple heuristics. They cannot choose the best sample for model training in different stages. Inspired by "Think, Fast and Slow" (System 1 and System 2) in cognitive science, we propose a reward-guided sampling strategy called Adaptive Sample with Reward (ASR) to tackle this challenge. To the best of our knowledge, this is the first work utilizing reinforcement learning (RL) to address the sampling problem in representation learning. Our approach optimally adjusts the sampling process to achieve optimal performance. We explore geographical relationships among samples by distance-based sampling to maximize overall cumulative reward. We apply ASR to the long-standing sampling problems in similarity-based loss functions. Empirical results in information retrieval and clustering demonstrate ASR's superb performance across different datasets. We also discuss an engrossing phenomenon which we name as "ASR gravity well" in experiments.

We study the problem of adaptively identifying patient subpopulations that benefit from a given treatment during a confirmatory clinical trial. This type of adaptive clinical trial has been thoroughly studied in biostatistics, but has been allowed only limited adaptivity so far. Here, we aim to relax classical restrictions on such designs and investigate how to incorporate ideas from the recent machine learning literature on adaptive and online experimentation to make trials more flexible and efficient. We find that the unique characteristics of the subpopulation selection problem -- most importantly that (i) one is usually interested in finding subpopulations with any treatment benefit (and not necessarily the single subgroup with largest effect) given a limited budget and that (ii) effectiveness only has to be demonstrated across the subpopulation on average -- give rise to interesting challenges and new desiderata when designing algorithmic solutions. Building on these findings, we propose AdaGGI and AdaGCPI, two meta-algorithms for subpopulation construction. We empirically investigate their performance across a range of simulation scenarios and derive insights into their (dis)advantages across different settings.

This paper presents the Adaptive Personalized Control System (APECS) architecture, a novel framework for human-in-the-loop control. An architecture is developed which defines appropriate constraints for the system objectives. A method for enacting Lipschitz and sector bounds on the resulting controller is derived to ensure desirable control properties. An analysis of worst-case loss functions and the optimal loss function weighting is made to implement an effective training scheme. Finally, simulations are carried out to demonstrate the effectiveness of the proposed architecture. This architecture resulted in a 4.5% performance increase compared to the human operator and 9% to an unconstrained feedforward neural network trained in the same way.

We examine the problem of regret minimization when the learner is involved in a continuous game with other optimizing agents: in this case, if all players follow a no-regret algorithm, it is possible to achieve significantly lower regret relative to fully adversarial environments. We study this problem in the context of variationally stable games (a class of continuous games which includes all convex-concave and monotone games), and when the players only have access to noisy estimates of their individual payoff gradients. If the noise is additive, the game-theoretic and purely adversarial settings enjoy similar regret guarantees; however, if the noise is multiplicative, we show that the learners can, in fact, achieve constant regret. We achieve this faster rate via an optimistic gradient scheme with learning rate separation -- that is, the method's extrapolation and update steps are tuned to different schedules, depending on the noise profile. Subsequently, to eliminate the need for delicate hyperparameter tuning, we propose a fully adaptive method that attains nearly the same guarantees as its non-adapted counterpart, while operating without knowledge of either the game or of the noise profile.

The vast majority of modern deep learning models are trained with momentum-based first-order optimizers. The momentum term governs the optimizer's memory by determining how much each past gradient contributes to the current convergence direction. Fundamental momentum methods, such as Nesterov Accelerated Gradient and the Heavy Ball method, as well as more recent optimizers such as AdamW and Lion, all rely on the momentum coefficient that is customarily set to β= 0.9 and kept constant during model training, a strategy widely used by practitioners, yet suboptimal. In this paper, we introduce an adaptive memory mechanism that replaces constant momentum with a dynamic momentum coefficient that is adjusted online during optimization. We derive our method by approximating the objective function using two planes: one derived from the gradient at the current iterate and the other obtained from the accumulated memory of the past gradients. To the best of our knowledge, such a proximal framework was never used for momentum-based optimization. Our proposed approach is novel, extremely simple to use, and does not rely on extra assumptions or hyperparameter tuning. We implement adaptive memory variants of both SGD and AdamW across a wide range of learning tasks, from simple convex problems to large-scale deep learning scenarios, demonstrating that our approach can outperform standard SGD and Adam with hand-tuned momentum coefficients. Finally, our work opens doors for new ways of inducing adaptivity in optimization.

We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty value. These training methods are particularly relevant for active learning and data subset selection problems. For SGD with a constant step size update, we present convergence results for linear classifiers and linearly separable datasets using squared hinge loss and similar training loss functions. Additionally, we extend our analysis to more general classifiers and datasets, considering a wide range of loss-based sampling strategies and smooth convex training loss functions. We propose a novel algorithm called Adaptive-Weight Sampling (AWS) that utilizes SGD with an adaptive step size that achieves stochastic Polyak's step size in expectation. We establish convergence rate results for AWS for smooth convex training loss functions. Our numerical experiments demonstrate the efficiency of AWS on various datasets by using either exact or estimated loss values.

We study contextual combinatorial bandits with probabilistically triggered arms (C^2MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C^2-UCB-T algorithm and propose a novel analysis that achieves an O(dKT) regret bound, removing a potentially exponentially large factor O(1/p_{min}), where d is the dimension of contexts, p_{min} is the minimum positive probability that any arm can be triggered, and batch-size K is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC^2-UCB and derive a regret bound O(dT), which is independent of the batch-size K. As a valuable by-product, our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C^2MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets.

We present a bag of tricks framework for few-shot class-incremental learning (FSCIL), which is a challenging form of continual learning that involves continuous adaptation to new tasks with limited samples. FSCIL requires both stability and adaptability, i.e., preserving proficiency in previously learned tasks while learning new ones. Our proposed bag of tricks brings together eight key and highly influential techniques that improve stability, adaptability, and overall performance under a unified framework for FSCIL. We organize these tricks into three categories: stability tricks, adaptability tricks, and training tricks. Stability tricks aim to mitigate the forgetting of previously learned classes by enhancing the separation between the embeddings of learned classes and minimizing interference when learning new ones. On the other hand, adaptability tricks focus on the effective learning of new classes. Finally, training tricks improve the overall performance without compromising stability or adaptability. We perform extensive experiments on three benchmark datasets, CIFAR-100, CUB-200, and miniIMageNet, to evaluate the impact of our proposed framework. Our detailed analysis shows that our approach substantially improves both stability and adaptability, establishing a new state-of-the-art by outperforming prior works in the area. We believe our method provides a go-to solution and establishes a robust baseline for future research in this area.

The choice of batch sizes in stochastic gradient optimizers is critical for model training. However, the practice of varying batch sizes throughout the training process is less explored compared to other hyperparameters. We investigate adaptive batch size strategies derived from adaptive sampling methods, traditionally applied only in stochastic gradient descent. Given the significant interplay between learning rates and batch sizes, and considering the prevalence of adaptive gradient methods in deep learning, we emphasize the need for adaptive batch size strategies in these contexts. We introduce AdAdaGrad and its scalar variant AdAdaGradNorm, which incrementally increase batch sizes during training, while model updates are performed using AdaGrad and AdaGradNorm. We prove that AdaGradNorm converges with high probability at a rate of O(1/K) for finding a first-order stationary point of smooth nonconvex functions within K iterations. AdaGrad also demonstrates similar convergence properties when integrated with a novel coordinate-wise variant of our adaptive batch size strategies. Our theoretical claims are supported by numerical experiments on various image classification tasks, highlighting the enhanced adaptability of progressive batching protocols in deep learning and the potential of such adaptive batch size strategies with adaptive gradient optimizers in large-scale model training.

In this paper, we provide a general framework for studying multi-agent online learning problems in the presence of delays and asynchronicities. Specifically, we propose and analyze a class of adaptive dual averaging schemes in which agents only need to accumulate gradient feedback received from the whole system, without requiring any between-agent coordination. In the single-agent case, the adaptivity of the proposed method allows us to extend a range of existing results to problems with potentially unbounded delays between playing an action and receiving the corresponding feedback. In the multi-agent case, the situation is significantly more complicated because agents may not have access to a global clock to use as a reference point; to overcome this, we focus on the information that is available for producing each prediction rather than the actual delay associated with each feedback. This allows us to derive adaptive learning strategies with optimal regret bounds, even in a fully decentralized, asynchronous environment. Finally, we also analyze an "optimistic" variant of the proposed algorithm which is capable of exploiting the predictability of problems with a slower variation and leads to improved regret bounds.

The assessment of safety performance plays a pivotal role in the development and deployment of connected and automated vehicles (CAVs). A common approach involves designing testing scenarios based on prior knowledge of CAVs (e.g., surrogate models), conducting tests in these scenarios, and subsequently evaluating CAVs' safety performances. However, substantial differences between CAVs and the prior knowledge can significantly diminish the evaluation efficiency. In response to this issue, existing studies predominantly concentrate on the adaptive design of testing scenarios during the CAV testing process. Yet, these methods have limitations in their applicability to high-dimensional scenarios. To overcome this challenge, we develop an adaptive testing environment that bolsters evaluation robustness by incorporating multiple surrogate models and optimizing the combination coefficients of these surrogate models to enhance evaluation efficiency. We formulate the optimization problem as a regression task utilizing quadratic programming. To efficiently obtain the regression target via reinforcement learning, we propose the dense reinforcement learning method and devise a new adaptive policy with high sample efficiency. Essentially, our approach centers on learning the values of critical scenes displaying substantial surrogate-to-real gaps. The effectiveness of our method is validated in high-dimensional overtaking scenarios, demonstrating that our approach achieves notable evaluation efficiency.

Large language models split into two families: reasoning-centric LLMs, which strengthen internal chain-of-thought reasoning but cannot invoke external tools, and agentic LLMs, which learn to interact with environments and leverage tools but often lag in deep reasoning. This divide arises from fundamentally different training objectives, leading to mismatched strengths and inefficiency on simple queries, where both families tend to overthink or over-call tools. In this work, we present Adaptive Agent Foundation Model (A^2FM), a unified framework that follows a route-then-align principle: the model first learns task-aware routing and then aligns mode-specific trajectories under a shared backbone. To address the inefficiency gap, we introduce a third mode-instant-that handles simple queries directly, preventing unnecessary reasoning or tool calls while complementing the agentic and reasoning modes. To jointly enhance accuracy and efficiency, we propose Adaptive Policy Optimization (APO), which enforces adaptive sampling across modes and applies a cost-regularized reward. On the 32B scale, A^2FM achieves 13.4% on BrowseComp, 70.4% on AIME25, and 16.7% on HLE, setting new SOTA among comparable models and performing competitively with frontier LLMs across agentic, reasoning, and general benchmarks. Notably, the adaptive execution achieves a cost of pass of only $0.00487 per correct answer-cutting cost by 45.2% relative to reasoning and 33.5% relative to agentic, thus delivering substantially higher cost efficiency while maintaining comparable accuracy.

Efficiently and flexibly estimating treatment effect heterogeneity is an important task in a wide variety of settings ranging from medicine to marketing, and there are a considerable number of promising conditional average treatment effect estimators currently available. These, however, typically rely on the assumption that the measured covariates are enough to justify conditional exchangeability. We propose the P-learner, motivated by the R- and DR-learner, a tailored two-stage loss function for learning heterogeneous treatment effects in settings where exchangeability given observed covariates is an implausible assumption, and we wish to rely on proxy variables for causal inference. Our proposed estimator can be implemented by off-the-shelf loss-minimizing machine learning methods, which in the case of kernel regression satisfies an oracle bound on the estimated error as long as the nuisance components are estimated reasonably well.

Task robust adaptation is a long-standing pursuit in sequential decision-making. Some risk-averse strategies, e.g., the conditional value-at-risk principle, are incorporated in domain randomization or meta reinforcement learning to prioritize difficult tasks in optimization, which demand costly intensive evaluations. The efficiency issue prompts the development of robust active task sampling to train adaptive policies, where risk-predictive models are used to surrogate policy evaluation. This work characterizes the optimization pipeline of robust active task sampling as a Markov decision process, posits theoretical and practical insights, and constitutes robustness concepts in risk-averse scenarios. Importantly, we propose an easy-to-implement method, referred to as Posterior and Diversity Synergized Task Sampling (PDTS), to accommodate fast and robust sequential decision-making. Extensive experiments show that PDTS unlocks the potential of robust active task sampling, significantly improves the zero-shot and few-shot adaptation robustness in challenging tasks, and even accelerates the learning process under certain scenarios. Our project website is at https://thu-rllab.github.io/PDTS_project_page.

Matrix-based optimizers have attracted growing interest for improving LLM training efficiency, with significant progress centered on orthogonalization/whitening based methods. While yielding substantial performance gains, a fundamental question arises: can we develop new paradigms beyond orthogonalization, pushing the efficiency frontier further? We present Adaptively Rotated Optimization (ARO, a new matrix optimization framework that treats gradient rotation as a first class design principle. ARO accelerates LLM training by performing normed steepest descent in a rotated coordinate system, where the rotation is determined by a novel norm-informed policy. This perspective yields update rules that go beyond existing orthogonalization and whitening optimizers, improving sample efficiency in practice. To make comparisons reliable, we propose a rigorously controlled benchmarking protocol that reduces confounding and bias. Under this protocol, ARO consistently outperforms AdamW (by 1.3 sim1.35times) and orthogonalization methods (by 1.1sim1.15times) in LLM pretraining at up to 8B activated parameters, and up to 8times overtrain budget, without evidence of diminishing returns. Finally, we discuss how ARO can be reformulated as a symmetry-aware optimizer grounded in rotational symmetries of residual streams, motivating advanced designs that enable computationally efficient exploitation of cross-layer/cross module couplings.

Machine learning models often experience performance degradation post-deployment due to shifts in data distribution. It is challenging to assess model's performance accurately when labels are missing or delayed. Existing proxy methods, such as drift detection, fail to measure the effects of these shifts adequately. To address this, we introduce a new method, Probabilistic Adaptive Performance Estimation (PAPE), for evaluating classification models on unlabeled data that accurately quantifies the impact of covariate shift on model performance. It is model and data-type agnostic and works for various performance metrics. Crucially, PAPE operates independently of the original model, relying only on its predictions and probability estimates, and does not need any assumptions about the nature of the covariate shift, learning directly from data instead. We tested PAPE on tabular data using over 900 dataset-model combinations created from US census data, assessing its performance against multiple benchmarks. Overall, PAPE provided more accurate performance estimates than other evaluated methodologies.

Mainstream Test-Time Adaptation (TTA) methods for adapting vision-language models, e.g., CLIP, typically rely on Shannon Entropy (SE) at test time to measure prediction uncertainty and inconsistency. However, since CLIP has a built-in bias from pretraining on highly imbalanced web-crawled data, SE inevitably results in producing biased estimates of uncertainty entropy. To address this issue, we notably find and demonstrate that Tsallis Entropy (TE), a generalized form of SE, is naturally suited for characterizing biased distributions by introducing a non-extensive parameter q, with the performance of SE serving as a lower bound for TE. Building upon this, we generalize TE into Adaptive Debiasing Tsallis Entropy (ADTE) for TTA, customizing a class-specific parameter q^l derived by normalizing the estimated label bias from continuously incoming test instances, for each category. This adaptive approach allows ADTE to accurately select high-confidence views and seamlessly integrate with a label adjustment strategy to enhance adaptation, without introducing distribution-specific hyperparameter tuning. Besides, our investigation reveals that both TE and ADTE can serve as direct, advanced alternatives to SE in TTA, without any other modifications. Experimental results show that ADTE outperforms state-of-the-art methods on ImageNet and its five variants, and achieves the highest average performance on 10 cross-domain benchmarks, regardless of the model architecture or text prompts used. Our code is available at https://github.com/Jinx630/ADTE.

Adaptive optimization is critical in federated learning, where enabling adaptivity on both the server and client sides has proven essential for achieving optimal performance. However, the scalability of such jointly adaptive systems is often hindered by resource limitations in communication and memory. In this paper, we introduce a class of efficient adaptive algorithms, named FedAda^2 and its enhanced version FedAda^2++, designed specifically for large-scale, cross-device federated environments. FedAda^2 optimizes communication efficiency by avoiding the transfer of preconditioners between the server and clients. Additionally, FedAda^2++ extends this approach by incorporating memory-efficient adaptive optimizers on the client side, further reducing on-device memory usage. Theoretically, we demonstrate that FedAda^2 and FedAda^2++ achieve the same convergence rates for general, non-convex objectives as its more resource-intensive counterparts that directly integrate joint adaptivity. Extensive empirical evaluations on image and text datasets demonstrate both the advantages of joint adaptivity and the effectiveness of FedAda^2/FedAda^2++.

Large language models are typically aligned with human preferences by optimizing reward models (RMs) fitted to human feedback. However, human preferences are multi-faceted, and it is increasingly common to derive reward from a composition of simpler reward models which each capture a different aspect of language quality. This itself presents a challenge, as it is difficult to appropriately weight these component RMs when combining them. Compounding this difficulty, because any RM is only a proxy for human evaluation, this process is vulnerable to overoptimization, wherein past a certain point, accumulating higher reward is associated with worse human ratings. In this paper, we perform, to our knowledge, the first study on overoptimization in composite RMs, showing that correlation between component RMs has a significant effect on the locations of these points. We then introduce an approach to solve this issue using constrained reinforcement learning as a means of preventing the agent from exceeding each RM's threshold of usefulness. Our method addresses the problem of weighting component RMs by learning dynamic weights, naturally expressed by Lagrange multipliers. As a result, each RM stays within the range at which it is an effective proxy, improving evaluation performance. Finally, we introduce an adaptive method using gradient-free optimization to identify and optimize towards these points during a single run.

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

Reinforcement Learning with Verifiable Rewards (RLVR) can elicit strong multi-step reasoning, yet it often encourages overly verbose traces. Moreover, naive length penalties in group-relative optimization can severely hurt accuracy. We attribute this failure to two structural issues: (i) Dilution of Length Baseline, where incorrect responses (with zero length reward) depress the group baseline and over-penalize correct solutions; and (ii) Difficulty-Penalty Mismatch, where a static penalty cannot adapt to problem difficulty, suppressing necessary reasoning on hard instances while leaving redundancy on easy ones. We propose Dynamic Decoupled Conditional Advantage (DDCA) to decouple efficiency optimization from correctness. DDCA computes length advantages conditionally within the correct-response cluster to eliminate baseline dilution, and dynamically scales the penalty strength using the group pass rate as a proxy for difficulty. Experiments on GSM8K, MATH500, AMC23, and AIME25 show that DDCA consistently improves the efficiency--accuracy trade-off relative to adaptive baselines, reducing generated tokens by approximately 60% on simpler tasks (e.g., GSM8K) versus over 20% on harder benchmarks (e.g., AIME25), thereby maintaining or improving accuracy. Code is available at https://github.com/alphadl/DDCA.

Model-agnostic meta-reinforcement learning requires estimating the Hessian matrix of value functions. This is challenging from an implementation perspective, as repeatedly differentiating policy gradient estimates may lead to biased Hessian estimates. In this work, we provide a unifying framework for estimating higher-order derivatives of value functions, based on off-policy evaluation. Our framework interprets a number of prior approaches as special cases and elucidates the bias and variance trade-off of Hessian estimates. This framework also opens the door to a new family of estimates, which can be easily implemented with auto-differentiation libraries, and lead to performance gains in practice.

The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel epsilon-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that epsilon-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g., EI and UCB), particularly with a limited budget. In higher dimensions epsilon-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution.

Foundation models are transitioning from offline predictors to deployed systems expected to operate over long time horizons. In real deployments, objectives are not fixed: domains drift, user preferences evolve, and new tasks appear after the model has shipped. This elevates continual learning and instant personalization from optional features to core architectural requirements. Yet most adaptation pipelines still follow a static weight paradigm: after training (or after any adaptation step), inference executes a single parameter vector regardless of user intent, domain, or instance-specific constraints. This treats the trained or adapted model as a single point in parameter space. In heterogeneous and continually evolving regimes, distinct objectives can induce separated feasible regions over parameters, forcing any single shared update into compromise, interference, or overspecialization. As a result, continual learning and personalization are often implemented as repeated overwriting of shared weights, risking degradation of previously learned behaviors. We propose HY-WU (Weight Unleashing), a memory-first adaptation framework that shifts adaptation pressure away from overwriting a single shared parameter point. HY-WU implements functional (operator-level) memory as a neural module: a generator that synthesizes weight updates on-the-fly from the instance condition, yielding instance-specific operators without test-time optimization.

Increasing the thinking budget of AI models can significantly improve accuracy, but not all questions warrant the same amount of reasoning. Users may prefer to allocate different amounts of reasoning effort depending on how they value output quality versus latency and cost. To leverage this tradeoff effectively, users need fine-grained control over the amount of thinking used for a particular query, but few approaches enable such control. Existing methods require users to specify the absolute number of desired tokens, but this requires knowing the difficulty of the problem beforehand to appropriately set the token budget for a query. To address these issues, we propose Adaptive Effort Control, a self-adaptive reinforcement learning method that trains models to use a user-specified fraction of tokens relative to the current average chain-of-thought length for each query. This approach eliminates dataset- and phase-specific tuning while producing better cost-accuracy tradeoff curves compared to standard methods. Users can dynamically adjust the cost-accuracy trade-off through a continuous effort parameter specified at inference time. We observe that the model automatically learns to allocate resources proportionally to the task difficulty and, across model scales ranging from 1.5B to 32B parameters, our approach enables a 2-3x reduction in chain-of-thought length while maintaining or improving performance relative to the base model used for RL training.

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.

Large language models (LLMs) are increasingly used as evaluators in lieu of humans. While scalable, their judgments are noisy due to imperfect specificity and sensitivity of LLMs, leading to biased accuracy estimates. Although bias-correction methods exist, they are underutilized in LLM research and typically assume exact knowledge of the model's specificity and sensitivity. Furthermore, in general we only have estimates of these values and it is not well known how to properly construct confidence intervals using only estimates. This work presents a simple plug-in framework that corrects such bias and constructs confidence intervals reflecting uncertainty from both test and calibration dataset, enabling practical and statistically sound LLM-based evaluation. Additionally, to reduce uncertainty in the accuracy estimate, we introduce an adaptive algorithm that efficiently allocates calibration sample sizes.

Users of music streaming, video streaming, news recommendation, and e-commerce services often engage with content in a sequential manner. Providing and evaluating good sequences of recommendations is therefore a central problem for these services. Prior reweighting-based counterfactual evaluation methods either suffer from high variance or make strong independence assumptions about rewards. We propose a new counterfactual estimator that allows for sequential interactions in the rewards with lower variance in an asymptotically unbiased manner. Our method uses graphical assumptions about the causal relationships of the slate to reweight the rewards in the logging policy in a way that approximates the expected sum of rewards under the target policy. Extensive experiments in simulation and on a live recommender system show that our approach outperforms existing methods in terms of bias and data efficiency for the sequential track recommendations problem.

We study how to learn ε-optimal strategies in zero-sum imperfect information games (IIG) with trajectory feedback. In this setting, players update their policies sequentially based on their observations over a fixed number of episodes, denoted by T. Existing procedures suffer from high variance due to the use of importance sampling over sequences of actions (Steinberger et al., 2020; McAleer et al., 2022). To reduce this variance, we consider a fixed sampling approach, where players still update their policies over time, but with observations obtained through a given fixed sampling policy. Our approach is based on an adaptive Online Mirror Descent (OMD) algorithm that applies OMD locally to each information set, using individually decreasing learning rates and a regularized loss. We show that this approach guarantees a convergence rate of mathcal{O}(T^{-1/2}) with high probability and has a near-optimal dependence on the game parameters when applied with the best theoretical choices of learning rates and sampling policies. To achieve these results, we generalize the notion of OMD stabilization, allowing for time-varying regularization with convex increments.

Adaptive gradient-based optimizers, particularly Adam, have left their mark in training large-scale deep learning models. The strength of such optimizers is that they exhibit fast convergence while being more robust to hyperparameter choice. However, they often generalize worse than non-adaptive methods. Recent studies have tied this performance gap to flat minima selection: adaptive methods tend to find solutions in sharper basins of the loss landscape, which in turn hurts generalization. To overcome this issue, we propose a new memory-augmented version of Adam that promotes exploration towards flatter minima by using a buffer of critical momentum terms during training. Intuitively, the use of the buffer makes the optimizer overshoot outside the basin of attraction if it is not wide enough. We empirically show that our method improves the performance of several variants of Adam on standard supervised language modelling and image classification tasks.

We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret minimization algorithms from the online learning literature to learn prediction sets with approximately valid coverage and small regret. However, standard regret minimization could be insufficient for handling changing environments, where performance guarantees may be desired not only over the full time horizon but also in all (sub-)intervals of time. We develop new online conformal prediction methods that minimize the strongly adaptive regret, which measures the worst-case regret over all intervals of a fixed length. We prove that our methods achieve near-optimal strongly adaptive regret for all interval lengths simultaneously, and approximately valid coverage. Experiments show that our methods consistently obtain better coverage and smaller prediction sets than existing methods on real-world tasks, such as time series forecasting and image classification under distribution shift.

This paper investigates the use of prior computation to estimate the value function to improve sample efficiency in on-policy policy gradient methods in reinforcement learning. Our approach is to estimate the value function from prior computations, such as from the Q-network learned in DQN or the value function trained for different but related environments. In particular, we learn a new value function for the target task while combining it with a value estimate from the prior computation. Finally, the resulting value function is used as a baseline in the policy gradient method. This use of a baseline has the theoretical property of reducing variance in gradient computation and thus improving sample efficiency. The experiments show the successful use of prior value estimates in various settings and improved sample efficiency in several tasks.

Our motivation is to shed light the performance of the widely popular "R-Learner." Like many other methods for estimating conditional average treatment effects (CATEs), R-Learning can be expressed as a weighted pseudo-outcome regression (POR). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. Specifically, we argue that R-Learning implicitly performs an inverse-variance weighted form of POR. These weights stabilize the regression and allow for convenient simplifications of bias terms.

Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost extra information to make better decisions. In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem. Assuming the learner has an oracle for the original optimization problem, we design a 2-competitive deterministic algorithm and a e/(e-1)-competitive randomized algorithm for buying information. We show that this ratio is tight as the problem is equivalent to a robust generalization of the ski-rental problem, which we call super-martingale stopping. We also consider an adaptive setting where the learner can choose to buy information after taking some actions for the underlying optimization problem. We focus on the classic optimization problem, Min-Sum Set Cover, where the goal is to quickly find an action that covers a given request drawn from a known distribution. We provide an 8-competitive algorithm running in polynomial time that chooses actions and decides when to buy information about the underlying request.

Retrieval-Augmented Generation (RAG) mitigates issues of the factual errors and hallucinated outputs generated by Large Language Models (LLMs) in open-domain question-answering tasks (OpenQA) via introducing external knowledge. For complex QA, however, existing RAG methods use LLMs to actively predict retrieval timing and directly use the retrieved information for generation, regardless of whether the retrieval timing accurately reflects the actual information needs, or sufficiently considers prior retrieved knowledge, which may result in insufficient information gathering and interaction, yielding low-quality answers. To address these, we propose a generic RAG approach called Adaptive Note-Enhanced RAG (Adaptive-Note) for complex QA tasks, which includes the iterative information collector, adaptive memory reviewer, and task-oriented generator, while following a new Retriever-and-Memory paradigm. Specifically, Adaptive-Note introduces an overarching view of knowledge growth, iteratively gathering new information in the form of notes and updating them into the existing optimal knowledge structure, enhancing high-quality knowledge interactions. In addition, we employ an adaptive, note-based stop-exploration strategy to decide "what to retrieve and when to stop" to encourage sufficient knowledge exploration. We conduct extensive experiments on five complex QA datasets, and the results demonstrate the superiority and effectiveness of our method and its components. The code and data are at https://github.com/thunlp/Adaptive-Note.

Reinforcement Learning with Verifiable Rewards (RLVR) is commonly based on group sampling to estimate advantages and stabilize policy updates. In practice, large group sizes are not feasible due to computational limits, which biases learning toward trajectories that are already likely. Smaller groups often miss rare-correct trajectories while still containing mixed rewards, concentrating probability on common solutions. We derive the probability that updates miss rare-correct modes as a function of group size, showing non-monotonic behavior, and characterize how updates redistribute mass within the correct set, revealing that unsampled-correct mass can shrink even as total correct mass grows. Motivated by this analysis, we propose a difficulty-aware advantage scaling coefficient, inspired by Focal loss, that down-weights updates on high-success prompts. The lightweight modification can be directly integrated into any group-relative RLVR algorithm such as GRPO, DAPO, and CISPO. On Qwen2.5-7B across in-domain and out-of-domain benchmarks, our method improves pass@256 from 64.1 rightarrow 70.3 (GRPO), 69.3 rightarrow 72.5 (DAPO), and 73.2 rightarrow 76.8 (CISPO), while preserving or improving pass@1, without increasing group size or computational cost.

Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via token-level entropy or sequence-level length control, they lack a semantically grounded, step-level measure of reasoning progress. As a result, LLMs fail to distinguish necessary deduction from redundant verification: they may continue checking after reaching a correct solution and, in extreme cases, overturn a correct trajectory into an incorrect final answer. To remedy the lack of process supervision, we introduce a training-free probing mechanism that extracts intermediate confidence and correctness and combines them into a Step Potential signal that explicitly estimates the reasoning state at each step. Building on this signal, we propose Step Potential Advantage Estimation (SPAE), a fine-grained credit assignment method that amplifies potential gains, penalizes potential drops, and applies penalty after potential saturates to encourage timely termination. Experiments across multiple benchmarks show SPAE consistently improves accuracy while substantially reducing response length, outperforming strong RL baselines and recent efficient reasoning and token-level advantage estimation methods. The code is available at https://github.com/cii030/SPAE-RL.

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals' outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that involves retrospective reshuffling of participants across experimental arms at the end of an RCT. We identify conditions under which such reassignments are permissible and can be leveraged to construct counterfactual trials, whose outcomes can be accurately ascertained, for free. We prove theoretically that such an estimator is more accurate than common estimators based on sample means -- we show that it returns an unbiased estimate and simultaneously reduces variance. We demonstrate the value of our approach through empirical experiments on synthetic, semi-synthetic as well as real case study data and show improved estimation accuracy across the board.

Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared with SGD or even fail to converge due to unstable and extreme learning rates. Recent work has put forward some algorithms such as AMSGrad to tackle this issue but they failed to achieve considerable improvement over existing methods. In our paper, we demonstrate that extreme learning rates can lead to poor performance. We provide new variants of Adam and AMSGrad, called AdaBound and AMSBound respectively, which employ dynamic bounds on learning rates to achieve a gradual and smooth transition from adaptive methods to SGD and give a theoretical proof of convergence. We further conduct experiments on various popular tasks and models, which is often insufficient in previous work. Experimental results show that new variants can eliminate the generalization gap between adaptive methods and SGD and maintain higher learning speed early in training at the same time. Moreover, they can bring significant improvement over their prototypes, especially on complex deep networks. The implementation of the algorithm can be found at https://github.com/Luolc/AdaBound .

Large Language Models (LLMs) have revolutionized natural language processing, yet aligning these models with human values and preferences using RLHF remains a significant challenge. This challenge is characterized by various instabilities, such as reward hacking and catastrophic forgetting. In this technical report, we propose two innovations to stabilize RLHF training: 1) Advantage Model, which directly models advantage score i.e., extra reward compared to the expected rewards and regulates score distributions across tasks to prevent reward hacking. 2) Selective Rehearsal, which mitigates catastrophic forgetting by strategically selecting data for PPO training and knowledge rehearsing. Our experimental analysis on public and proprietary datasets reveals that the proposed methods not only increase stability in RLHF training but also achieve higher reward scores and win rates.

This paper develops a policy learning method for tuning a pre-trained policy to adapt to additional tasks without altering the original task. A method named Adaptive Policy Gradient (APG) is proposed in this paper, which combines Bellman's principle of optimality with the policy gradient approach to improve the convergence rate. This paper provides theoretical analysis which guarantees the convergence rate and sample complexity of O(1/T) and O(1/epsilon), respectively, where T denotes the number of iterations and epsilon denotes the accuracy of the resulting stationary policy. Furthermore, several challenging numerical simulations, including cartpole, lunar lander, and robot arm, are provided to show that APG obtains similar performance compared to existing deterministic policy gradient methods while utilizing much less data and converging at a faster rate.

We examine a simple stochastic strategy for adapting well-known single-point acquisition functions to allow batch active learning. Unlike acquiring the top-K points from the pool set, score- or rank-based sampling takes into account that acquisition scores change as new data are acquired. This simple strategy for adapting standard single-sample acquisition strategies can even perform just as well as compute-intensive state-of-the-art batch acquisition functions, like BatchBALD or BADGE, while using orders of magnitude less compute. In addition to providing a practical option for machine learning practitioners, the surprising success of the proposed method in a wide range of experimental settings raises a difficult question for the field: when are these expensive batch acquisition methods pulling their weight?

In the field of algorithmic fairness, significant attention has been put on group fairness criteria, such as Demographic Parity and Equalized Odds. Nevertheless, these objectives, measured as global averages, have raised concerns about persistent local disparities between sensitive groups. In this work, we address the problem of local fairness, which ensures that the predictor is unbiased not only in terms of expectations over the whole population, but also within any subregion of the feature space, unknown at training time. To enforce this objective, we introduce ROAD, a novel approach that leverages the Distributionally Robust Optimization (DRO) framework within a fair adversarial learning objective, where an adversary tries to infer the sensitive attribute from the predictions. Using an instance-level re-weighting strategy, ROAD is designed to prioritize inputs that are likely to be locally unfair, i.e. where the adversary faces the least difficulty in reconstructing the sensitive attribute. Numerical experiments demonstrate the effectiveness of our method: it achieves Pareto dominance with respect to local fairness and accuracy for a given global fairness level across three standard datasets, and also enhances fairness generalization under distribution shift.

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

This paper investigates the evaluation of learned multiagent strategies in the incomplete information setting, which plays a critical role in ranking and training of agents. Traditionally, researchers have relied on Elo ratings for this purpose, with recent works also using methods based on Nash equilibria. Unfortunately, Elo is unable to handle intransitive agent interactions, and other techniques are restricted to zero-sum, two-player settings or are limited by the fact that the Nash equilibrium is intractable to compute. Recently, a ranking method called α-Rank, relying on a new graph-based game-theoretic solution concept, was shown to tractably apply to general games. However, evaluations based on Elo or α-Rank typically assume noise-free game outcomes, despite the data often being collected from noisy simulations, making this assumption unrealistic in practice. This paper investigates multiagent evaluation in the incomplete information regime, involving general-sum many-player games with noisy outcomes. We derive sample complexity guarantees required to confidently rank agents in this setting. We propose adaptive algorithms for accurate ranking, provide correctness and sample complexity guarantees, then introduce a means of connecting uncertainties in noisy match outcomes to uncertainties in rankings. We evaluate the performance of these approaches in several domains, including Bernoulli games, a soccer meta-game, and Kuhn poker.

Testing and evaluation is a critical step in the development and deployment of connected and automated vehicles (CAVs). Due to the black-box property and various types of CAVs, how to test and evaluate CAVs adaptively remains a major challenge. Many approaches have been proposed to adaptively generate testing scenarios during the testing process. However, most existing approaches cannot be applied to complex scenarios, where the variables needed to define such scenarios are high dimensional. Towards filling this gap, the adaptive testing with sparse control variates method is proposed in this paper. Instead of adaptively generating testing scenarios, our approach evaluates CAVs' performances by adaptively utilizing the testing results. Specifically, each testing result is adjusted using multiple linear regression techniques based on control variates. As the regression coefficients can be adaptively optimized for the CAV under test, using the adjusted results can reduce the estimation variance, compared with using the testing results directly. To overcome the high dimensionality challenge, sparse control variates are utilized only for the critical variables of testing scenarios. To validate the proposed method, the high-dimensional overtaking scenarios are investigated, and the results demonstrate that our approach can further accelerate the evaluation process by about 30 times.

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.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. Leveraging the structure of the learning problem, we argue that multi-environment generalization can be achieved using a simpler learning model, with an affine structure with respect to the learning task. Crucially, we prove that this architecture can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to physical-parameter-induced adaptation and to adaptive control.

Adaptive optimization methods are widely recognized as among the most popular approaches for training Deep Neural Networks (DNNs). Techniques such as Adam, AdaGrad, and AdaHessian utilize a preconditioner that modifies the search direction by incorporating information about the curvature of the objective function. However, despite their adaptive characteristics, these methods still require manual fine-tuning of the step-size. This, in turn, impacts the time required to solve a particular problem. This paper presents an optimization framework named SANIA to tackle these challenges. Beyond eliminating the need for manual step-size hyperparameter settings, SANIA incorporates techniques to address poorly scaled or ill-conditioned problems. We also explore several preconditioning methods, including Hutchinson's method, which approximates the Hessian diagonal of the loss function. We conclude with an extensive empirical examination of the proposed techniques across classification tasks, covering both convex and non-convex contexts.

Continual learning is an emerging subject in machine learning that aims to solve multiple tasks presented sequentially to the learner without forgetting previously learned tasks. Recently, many deep learning based approaches have been proposed for continual learning, however the mathematical foundations behind existing continual learning methods remain underdeveloped. On the other hand, adaptive filtering is a classic subject in signal processing with a rich history of mathematically principled methods. However, its role in understanding the foundations of continual learning has been underappreciated. In this tutorial, we review the basic principles behind both continual learning and adaptive filtering, and present a comparative analysis that highlights multiple connections between them. These connections allow us to enhance the mathematical foundations of continual learning based on existing results for adaptive filtering, extend adaptive filtering insights using existing continual learning methods, and discuss a few research directions for continual learning suggested by the historical developments in adaptive filtering.

We propose a novel approach to addressing two fundamental challenges in Model-based Reinforcement Learning (MBRL): the computational expense of repeatedly finding a good policy in the learned model, and the objective mismatch between model fitting and policy computation. Our "lazy" method leverages a novel unified objective, Performance Difference via Advantage in Model, to capture the performance difference between the learned policy and expert policy under the true dynamics. This objective demonstrates that optimizing the expected policy advantage in the learned model under an exploration distribution is sufficient for policy computation, resulting in a significant boost in computational efficiency compared to traditional planning methods. Additionally, the unified objective uses a value moment matching term for model fitting, which is aligned with the model's usage during policy computation. We present two no-regret algorithms to optimize the proposed objective, and demonstrate their statistical and computational gains compared to existing MBRL methods through simulated benchmarks.

The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total value of the admitted items. Although optimal competitive algorithms are known for this problem, they may be fundamentally unfair, i.e., individual items may be treated inequitably in different ways. We formalize a practically-relevant notion of time fairness which effectively models a trade off between static and dynamic pricing in a motivating application such as cloud resource allocation, and show that existing algorithms perform poorly under this metric. We propose a parameterized deterministic algorithm where the parameter precisely captures the Pareto-optimal trade-off between fairness (static pricing) and competitiveness (dynamic pricing). We show that randomization is theoretically powerful enough to be simultaneously competitive and fair; however, it does not work well in experiments. To further improve the trade-off between fairness and competitiveness, we develop a nearly-optimal learning-augmented algorithm which is fair, consistent, and robust (competitive), showing substantial performance improvements in numerical experiments.

Plasticity, the ability of a neural network to evolve with new data, is crucial for high-performance and sample-efficient visual reinforcement learning (VRL). Although methods like resetting and regularization can potentially mitigate plasticity loss, the influences of various components within the VRL framework on the agent's plasticity are still poorly understood. In this work, we conduct a systematic empirical exploration focusing on three primary underexplored facets and derive the following insightful conclusions: (1) data augmentation is essential in maintaining plasticity; (2) the critic's plasticity loss serves as the principal bottleneck impeding efficient training; and (3) without timely intervention to recover critic's plasticity in the early stages, its loss becomes catastrophic. These insights suggest a novel strategy to address the high replay ratio (RR) dilemma, where exacerbated plasticity loss hinders the potential improvements of sample efficiency brought by increased reuse frequency. Rather than setting a static RR for the entire training process, we propose Adaptive RR, which dynamically adjusts the RR based on the critic's plasticity level. Extensive evaluations indicate that Adaptive RR not only avoids catastrophic plasticity loss in the early stages but also benefits from more frequent reuse in later phases, resulting in superior sample efficiency.

When fine-tuning pre-trained Large Language Models (LLMs) to align with human values and intentions, maximizing the estimated reward can lead to superior performance, but it also introduces potential risks due to deviations from the reference model's intended behavior. Most existing methods typically introduce KL divergence to constrain deviations between the trained model and the reference model; however, this may not be sufficient in certain applications that require tight risk control. In this paper, we introduce Risk-aware Direct Preference Optimization (Ra-DPO), a novel approach that incorporates risk-awareness by employing a class of nested risk measures. This approach formulates a constrained risk-aware advantage function maximization problem and then converts the Bradley-Terry model into a token-level representation. The objective function maximizes the likelihood of the policy while suppressing the deviation between a trained model and the reference model using a sequential risk ratio, thereby enhancing the model's risk-awareness. Experimental results across three open-source datasets: IMDb Dataset, Anthropic HH Dataset, and AlpacaEval, demonstrate the proposed method's superior performance in balancing alignment performance and model drift. Our code is opensourced at https://github.com/zlj123-max/Ra-DPO.

The recent surge in large-scale foundation models has spurred the development of efficient methods for adapting these models to various downstream tasks. Low-rank adaptation methods, such as LoRA, have gained significant attention due to their outstanding parameter efficiency and no additional inference latency. This paper investigates a more general form of adapter module based on the analysis that parallel and sequential adaptation branches learn novel and general features during fine-tuning, respectively. The proposed method, named Hydra, due to its multi-head computational branches, combines parallel and sequential branch to integrate capabilities, which is more expressive than existing single branch methods and enables the exploration of a broader range of optimal points in the fine-tuning process. In addition, the proposed adaptation method explicitly leverages the pre-trained weights by performing a linear combination of the pre-trained features. It allows the learned features to have better generalization performance across diverse downstream tasks. Furthermore, we perform a comprehensive analysis of the characteristics of each adaptation branch with empirical evidence. Through an extensive range of experiments, encompassing comparisons and ablation studies, we substantiate the efficiency and demonstrate the superior performance of Hydra. This comprehensive evaluation underscores the potential impact and effectiveness of Hydra in a variety of applications. Our code is available on https://github.com/extremebird/Hydra

Wild Test-Time Adaptation (WTTA) is proposed to adapt a source model to unseen domains under extreme data scarcity and multiple shifts. Previous approaches mainly focused on sample selection strategies, while overlooking the fundamental problem on underlying optimization. Initially, we critically analyze the widely-adopted entropy minimization framework in WTTA and uncover its significant limitations in noisy optimization dynamics that substantially hinder adaptation efficiency. Through our analysis, we identify region confidence as a superior alternative to traditional entropy, however, its direct optimization remains computationally prohibitive for real-time applications. In this paper, we introduce a novel region-integrated method ReCAP that bypasses the lengthy process. Specifically, we propose a probabilistic region modeling scheme that flexibly captures semantic changes in embedding space. Subsequently, we develop a finite-to-infinite asymptotic approximation that transforms the intractable region confidence into a tractable and upper-bounded proxy. These innovations significantly unlock the overlooked potential dynamics in local region in a concise solution. Our extensive experiments demonstrate the consistent superiority of ReCAP over existing methods across various datasets and wild scenarios.

We present Free energy Estimators with Adaptive Transport (FEAT), a novel framework for free energy estimation -- a critical challenge across scientific domains. FEAT leverages learned transports implemented via stochastic interpolants and provides consistent, minimum-variance estimators based on escorted Jarzynski equality and controlled Crooks theorem, alongside variational upper and lower bounds on free energy differences. Unifying equilibrium and non-equilibrium methods under a single theoretical framework, FEAT establishes a principled foundation for neural free energy calculations. Experimental validation on toy examples, molecular simulations, and quantum field theory demonstrates improvements over existing learning-based methods.

In the experts problem, on each of T days, an agent needs to follow the advice of one of n ``experts''. After each day, the loss associated with each expert's advice is revealed. A fundamental result in learning theory says that the agent can achieve vanishing regret, i.e. their cumulative loss is within o(T) of the cumulative loss of the best-in-hindsight expert. Can the agent perform well without sufficient space to remember all the experts? We extend a nascent line of research on this question in two directions: bullet We give a new algorithm against the oblivious adversary, improving over the memory-regret tradeoff obtained by [PZ23], and nearly matching the lower bound of [SWXZ22]. bullet We also consider an adaptive adversary who can observe past experts chosen by the agent. In this setting we give both a new algorithm and a novel lower bound, proving that roughly n memory is both necessary and sufficient for obtaining o(T) regret.

Existing reinforcement learning (RL)-based post-training methods for large language models have advanced rapidly, yet their design has largely been guided by heuristics rather than systematic theoretical principles. This gap limits our understanding of the properties of the gradient estimators and the associated optimization algorithms, thereby constraining opportunities to improve training stability and overall performance. In this work, we provide a unified theoretical framework that characterizes the statistical properties of commonly used policy-gradient estimators under mild assumptions. Our analysis establishes unbiasedness, derives exact variance expressions, and yields an optimization-loss upper bound that enables principled reasoning about learning dynamics. Building on these results, we prove convergence guarantees and derive an adaptive learning-rate schedule governed by the signal-to-noise ratio (SNR) of gradients. We further show that the variance-optimal baseline is a gradient-weighted estimator, offering a new principle for variance reduction and naturally enhancing stability beyond existing methods. These insights motivate Optimal Baseline and Learning-Rate Policy Optimization (OBLR-PO), an algorithm that jointly adapts learning rates and baselines in a theoretically grounded manner. Experiments on Qwen3-4B-Base and Qwen3-8B-Base demonstrate consistent gains over existing policy optimization methods, validating that our theoretical contributions translate into practical improvements in large-scale post-training.

The rapid proliferation of Large Language Models (LLMs) and diverse specialized benchmarks necessitates a shift from fragmented, task-specific metrics to a holistic, competitive ranking system that effectively aggregates performance across multiple ability dimensions. Primarily using static scoring, current evaluation methods are fundamentally limited. They struggle to determine the proper mix ratio across diverse benchmarks, and critically, they fail to capture a model's dynamic competitive fitness or its vulnerability when confronted with sequential, high-stakes tasks. To address this, we introduce the novel Competitive Swiss-System Dynamics (CSD) framework. CSD simulates a multi-round, sequential contest where models are dynamically paired across a curated sequence of benchmarks based on their accumulated win-loss record. And Monte Carlo Simulation (N=100,000 iterations) is used to approximate the statistically robust Expected Win Score (E[S_m]), which eliminates the noise of random pairing and early-round luck. Furthermore, we implement a Failure Sensitivity Analysis by parameterizing the per-round elimination quantity (T_k), which allows us to profile models based on their risk appetite--distinguishing between robust generalists and aggressive specialists. We demonstrate that CSD provides a more nuanced and context-aware ranking than traditional aggregate scoring and static pairwise models, representing a vital step towards risk-informed, next-generation LLM evaluation.

We give a new algorithm for best arm identification in linearly parameterised bandits in the fixed confidence setting. The algorithm generalises the well-known LUCB algorithm of Kalyanakrishnan et al. (2012) by playing an arm which minimises a suitable notion of geometric overlap of the statistical confidence set for the unknown parameter, and is fully adaptive and computationally efficient as compared to several state-of-the methods. We theoretically analyse the sample complexity of the algorithm for problems with two and three arms, showing optimality in many cases. Numerical results indicate favourable performance over other algorithms with which we compare.

While prior research has proposed a plethora of methods that build neural classifiers robust against adversarial robustness, practitioners are still reluctant to adopt them due to their unacceptably severe clean accuracy penalties. This paper significantly alleviates this accuracy-robustness trade-off by mixing the output probabilities of a standard classifier and a robust classifier, where the standard network is optimized for clean accuracy and is not robust in general. We show that the robust base classifier's confidence difference for correct and incorrect examples is the key to this improvement. In addition to providing intuitions and empirical evidence, we theoretically certify the robustness of the mixed classifier under realistic assumptions. Furthermore, we adapt an adversarial input detector into a mixing network that adaptively adjusts the mixture of the two base models, further reducing the accuracy penalty of achieving robustness. The proposed flexible method, termed "adaptive smoothing", can work in conjunction with existing or even future methods that improve clean accuracy, robustness, or adversary detection. Our empirical evaluation considers strong attack methods, including AutoAttack and adaptive attack. On the CIFAR-100 dataset, our method achieves an 85.21% clean accuracy while maintaining a 38.72% ell_infty-AutoAttacked (epsilon = 8/255) accuracy, becoming the second most robust method on the RobustBench CIFAR-100 benchmark as of submission, while improving the clean accuracy by ten percentage points compared with all listed models. The code that implements our method is available at https://github.com/Bai-YT/AdaptiveSmoothing.

In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known for multi-option ski rental, with or without learning augmentation. We present the first randomized learning-augmented algorithm for this problem, surpassing previous performance guarantees given by deterministic algorithms. Our learning-augmented algorithm is based on a new, provably best-possible randomized competitive algorithm for the problem. Our results are further complemented by lower bounds for deterministic and randomized algorithms, and computational experiments evaluating our algorithms' performance improvements.

We revisit Group Relative Policy Optimization (GRPO) in both on-policy and off-policy optimization regimes. Our motivation comes from recent work on off-policy Proximal Policy Optimization (PPO), which improves training stability, sampling efficiency, and memory usage. In addition, a recent analysis of GRPO suggests that estimating the advantage function with off-policy samples could be beneficial. Building on these observations, we adapt GRPO to the off-policy setting. We show that both on-policy and off-policy GRPO objectives yield an improvement in the reward. This result motivates the use of clipped surrogate objectives in the off-policy version of GRPO. We then compare the empirical performance of reinforcement learning with verifiable rewards in post-training using both GRPO variants. Our results show that off-policy GRPO either significantly outperforms or performs on par with its on-policy counterpart.

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but the question is how, and by how much? We show that the degree of improvement must depend on the quality of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given competence level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

Retrieval-augmented agents can query external evidence, yet their reliability in multi-step reasoning remains limited: noisy retrieval may derail multi-hop question answering, while outcome-only reinforcement learning provides credit signals that are too coarse to optimize intermediate steps. We propose EvalAct (Evaluate-as-Action), which converts implicit retrieval quality assessment into an explicit action and enforces a coupled Search-to-Evaluate protocol so that each retrieval is immediately followed by a structured evaluation score, yielding process signals aligned with the interaction trajectory. To leverage these signals, we introduce Process-Calibrated Advantage Rescaling (PCAR), a GRPO-based optimization method that rescales advantages at the segment level according to evaluation scores, emphasizing reliable segments while updating uncertain ones conservatively. Experiments on seven open-domain QA benchmarks show that EvalAct achieves the best average accuracy, with the largest gains on multi-hop tasks, and ablations verify that the explicit evaluation loop drives the primary improvements while PCAR provides consistent additional benefits.

In recent years, the state-of-the-art in deep learning has been dominated by very large models that have been pre-trained on vast amounts of data. The paradigm is very simple: Investing more computational resources (optimally) leads to better performance, and even predictably so; neural scaling laws have been derived that accurately forecast the performance of a network for a desired level of compute. This leads to the notion of a "compute-optimal" model, i.e. a model that allocates a given level of compute during training optimally to maximise performance. In this work, we extend the concept of optimality by allowing for an "adaptive" model, i.e. a model that can change its shape during the course of training. By allowing the shape to adapt, we can optimally traverse between the underlying scaling laws, leading to a significant reduction in the required compute to reach a given target performance. We focus on vision tasks and the family of Vision Transformers, where the patch size as well as the width naturally serve as adaptive shape parameters. We demonstrate that, guided by scaling laws, we can design compute-optimal adaptive models that beat their "static" counterparts.

We present Entropy Adaptive Decoding (EAD), a novel approach for efficient language model inference that dynamically switches between different-sized models based on prediction uncertainty. By monitoring rolling entropy in model logit distributions, our method identifies text regions where a smaller model suffices and switches to a larger model only when prediction uncertainty exceeds a threshold. Unlike speculative decoding approaches that maintain perfect output fidelity through verification, EAD accepts controlled output divergence in exchange for computational efficiency. Our experiments on the MATH benchmark demonstrate remarkable efficiency gains across different model families. Using the LLaMA family, we maintain 96.7\% of the 11B model's performance (50.4\% vs 52.1\%) while using it for only 43\% of tokens, decreasing computational cost by 41.5\%. These gains become more pronounced with larger size differentials in the Qwen family, where we achieve 92.9\% of the 14B model's performance (74.3\% vs 80.0\%) while using it for just 25\% of tokens, decreasing computational cost by 67\%. The consistency of these results across model pairs suggests that language model computation can be significantly optimized by selectively deploying model capacity based on local generation complexity. Our findings indicate that current approaches to model inference may be unnecessarily conservative in their pursuit of perfect output fidelity, and that accepting minor performance trade-offs can enable dramatic reductions in computational costs.