RL for Language Model Reasoning

RL: Reinforcement Learning

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91 papers in the last four weeks, up 176% on the four weeks before. 0.9% of all new papers.

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May 21, 2026cs.CL

LANG: Reinforcement Learning for Multilingual Reasoning with Language-Adaptive Hint Guidance

Reinforcement learning has proven effective for enhancing multi-step reasoning in large language models (LLMs), yet its benefits have not fully translated to multilingual contexts. Existing methods struggle with a fundamental trade-off: prioritizing input-language consistency severely hampers reasoning quality, while prioritizing reasoning often leads to unintended language drift toward English. We address this challenge with LANG, a novel framework that leverages language-conditioned hints to guide exploration in non-English reasoning tasks. Our method incorporates two key mechanisms to prevent dependency on these hints: a progressive decay schedule that gradually withdraws scaffolding, and a language-adaptive switch that tailors learning horizons to specific language difficulties. Empirical results on challenging multilingual mathematical benchmarks reveal that LANG substantially enhances reasoning performance without compromising language consistency. Moreover, we show that our framework generalizes beyond mathematics, fostering more consistent language alignment across model layers

Yuchun Fan, Bei Li, Peiguang Li +9

NLP Lab, School of Computer Science and Engineering, Northeastern University, Shenyang, China · Meituan Inc. 3NiuTrans Research, Shenyang, China

Multilingual Language Models Reinforcement Learning Cross-Lingual Reasoning in Language Models RL for Language Model Reasoning LLM Reasoning

May 21, 2026cs.AI

Search-E1: Self-Distillation Drives Self-Evolution in Search-Augmented Reasoning

Post-training has become the dominant recipe for turning a language model into a competent search-augmented reasoning agent. A line of recent work pushes its performance further by adding elaborate machinery on top of this standard pipeline. These augmentations import external supervision from stronger external systems, attach auxiliary modules such as process reward models or retrospective critics, restructure the rollout itself with tree search or multi-stage curricula, or shape the reward with hand-crafted bonuses and penalties. Each addition delivers a measurable gain, but each also inflates the training pipeline and ties the recipe to resources or designs that may not always be available. We take a step back and ask whether any of this machinery is actually necessary, and propose Search-E1, a self-evolution method that lets a search-augmented agent improve through only vanilla GRPO interleaved with on-policy self-distillation (OPSD). After each GRPO round, the policy rolls out on its own training questions. A token-level forward KL objective then aligns the policy's inference-time distribution to its own distribution under a privileged context that exposes a more efficient sibling trajectory. Despite this simplicity, the procedure naturally provides dense per-step supervision. On seven QA benchmarks, Search-E1 reaches 0.440 average EM with Qwen2.5-3B, surpassing all open-source baselines at both scales. Code and complete version will be made public soon.

Zihan Liang, Yufei Ma, Ben Chen +4

Tool-Augmented Language Model Agents On-Policy Self-Distillation RL for Language Model Reasoning LLM Agent Self-Improvement LLM Reasoning

May 21, 2026cs.LG

Survive or Collapse: The Asymmetric Roles of Data Gating and Reward Grounding in Self-Play RL

Self-play reinforcement learning trains language models on their own generated tasks, co-evolving a proposer and solver without human labels. Recent systems report strong reasoning gains, but collapse and instability are widely observed and poorly understood. The dominant response treats this as a reward-design problem. We argue instead that self-play stability is governed by two distinct levers: a data-level gate that decides which proposer-generated tasks enter the training pool, and the reward signal that updates the policy on tasks already admitted. Through controlled experiments on a Python output-prediction task and a deterministic-DSL twin task that strips pretraining priors, output ambiguity, and executor noise, we find the two levers are asymmetric. A strict gate is sufficient for stability under every reward variant we test, including a self-consistency reward with no access to ground truth; while no reward variant is sufficient once the gate is removed. This asymmetry exposes a counter-intuitive coupling we call the Grounded Proposer Paradox: a proposer with ground-truth access accelerates collapse faster than an ungrounded one when paired with a self-consistency solver, by concentrating training on clean tasks that form the fastest path to a spurious self-consistent attractor. Replacing the binary gate with a continuous strictness parameter

\varepsilon

further reveals a two-stage phase transition: training-side metrics decouple at low

\varepsilon

, while validation accuracy holds until

\varepsilon

is much higher. Data-level gating, not reward calibration, is the binding constraint on self-play stability.

Sophia Xiao Pu, Zhaotian Weng, Chengzhi Liu +4

University of California, Santa Barbara · Cisco Research

Reinforcement Learning Self-Play RL RL for Language Model Reasoning

May 21, 2026cs.AI

CLORE: Content-Level Optimization for Reasoning Efficiency

Reinforcement learning post-training has improved the reasoning ability of large language models, but often produces unnecessarily long, repetitive, or semantically opaque reasoning traces. Existing efficient reasoning methods mainly regulate response length through explicit budgets or length-aware rewards, leaving intermediate reasoning content weakly supervised. We propose CLORE, a content-level optimization framework that improves reasoning efficiency by editing correct on-policy rollouts. CLORE uses an external augmentation model to delete repetitive segments, illegible or task-irrelevant content, and superfluous reasoning after the solution is established, while preserving the final answer. The resulting augmented--original pairs are optimized with an auxiliary reference-free DPO objective alongside standard policy-gradient training. By restricting augmentation to correct trajectories and performing local deletion, CLORE keeps edited rollouts close to the policy distribution and mitigates off-policy mismatch. Experiments on DeepSeek-R1-Distill-Qwen-7B and Qwen2.5-Math-7B across five mathematical reasoning benchmarks show that CLORE improves the accuracy--efficiency trade-off and remains compatible with GRPO, DAPO, Training Efficient, and ThinkPrune. Content-level analyses further show that CLORE reduces repetitive reasoning, illegible content, and post-answer exploration, supporting content-level supervision as a complementary direction to length-level control.

Yuyang Wu, Qiyao Xue, Guanxing Lu +4

Carnegie Mellon University · University of North Carolina, Chapel Hill · University of Pittsburgh +1

RL for Language Model Reasoning Efficient Language Model Reasoning

May 21, 2026cs.LG

Reinforced Graph of Thoughts: RL-Driven Adaptive Prompting for LLMs

Graph of Thoughts (GoT), a generalized form of recent prompting paradigms for large language models (LLMs), has been shown to be useful for elaborate problem solving. By executing a graph of operations, thoughts of the LLM are structured as an arbitrary graph, forming the actual graph of thoughts. Originally, the graph of operations is defined manually, which requires in-depth knowledge about the solution of the problem to solve. Such a static graph of operations is rigid and therefore lacks adaptability. We propose Reinforced Graph of Thoughts (RGoT), an automated approach to the GoT prompting paradigm that leverages reinforcement learning (RL) to adaptively generate a graph of operations from a human-defined set. Results indicate that, under certain constraints, it is possible to construct graphs of operations adaptively to the task's complexity in an automated way.

Manuel Noah Riesen, Peter Alfred von Niederhäusern

School of Engineering and Computer Science Bern University of Applied Sciences Bern, Switzerland

LLM Reasoning with Graphs LLM Prompting CoT Reasoning RL for Language Model Reasoning

May 21, 2026cs.LG

From Reasoning Chains to Verifiable Subproblems: Curriculum Reinforcement Learning Enables Credit Assignment for LLM Reasoning

Reinforcement learning from verifiable rewards (RLVR) has shown strong promise for LLM reasoning, but outcome-based RLVR remains inefficient on hard problems because correct final-answer rollouts are rare and sample-level credit assignment cannot use partial progress in failed attempts. We introduce SCRL (Subproblem Curriculum Reinforcement Learning), a curriculum RL framework that derives verifiable subproblems from reference reasoning chains and fixes the final subproblem as the original problem. This turns partial progress on hard problems into verifiable learning signals. Algorithmically, SCRL uses subproblem-level normalization, which normalizes rewards independently at each subproblem position and assigns the resulting advantages to the corresponding answer spans, enabling finer-grained credit assignment without external rubrics or reward models. Our analysis shows that subproblem curricula lift hard problems out of gradient dead zones, with larger relative gains as the original problem becomes harder. Across seven mathematical reasoning benchmarks, SCRL outperforms strong curriculum-learning baselines, improving average accuracy over GRPO by +4.1 points on Qwen3-4B-Base and +1.9 points on Qwen3-14B-Base. On AIME24, AIME25, and IMO-Bench, SCRL further improves pass@1 by +3.7 points and pass@64 by +4.6 points on Qwen3-4B-Base, indicating better exploration on hard reasoning problems.

Xitai Jiang, Zihan Tang, Wenze Lin +3

LeapLab, Tsinghua University · Qiuzhen College, Tsinghua University · B Gao Huang

RL for Language Model Reasoning Credit Assignment in RL Step-Level Credit Assignment in RL Curriculum RL Reinforcement Learning with Verifiable Rewards LLM Mathematical Reasoning

May 21, 2026cs.LG

Reasoning through Verifiable Forecast Actions: Consistency-Grounded RL for Financial LLMs

Financial markets are characterized by extreme non-stationarity, low signal-to-noise ratios, and strong dependence on external information such as news, company fundamentals, and macroeconomic signals. Yet, existing approaches either abstract time-series into text or decouple forecasting from language-based reasoning, leading to a fundamental mismatch between qualitative reasoning and quantitative outcomes. To address this, we introduce StockR1, a time-series-enhanced LLM that unifies stock forecasting and financial reasoning through a verifiable forecast action. Based on a tool-call design, the model first emits a forecast action, which is a structured and interpretable representation of its qualitative market outlook. It then invokes a time-series decoder conditioned on this action to generate distributional future trajectories, leading to more informed question answering and financial reasoning. We optimize the full pipeline with reinforcement learning, where rewards jointly reflect answer validity, forecast accuracy, and consistency between generated actions and observed time-series dynamics. In addition, rewards are reweighted by a sample-level uncertainty scalar, encouraging the model to accommodate varying uncertainty in market dynamics. We evaluate StockR1 on financial question answering and stock forecasting over a large-scale 10-year benchmark. Our method consistently outperforms time-series baselines and general-purpose LLMs, improving reasoning accuracy by 17.7% (4B) and 25.9% (8B). These findings demonstrate that structuring the forecast actions establishes a powerful synergy between language reasoning and temporal prediction, enabling LLMs to reason through verifiable, interpretable, and numerically grounded decisions.

Jialin Chen, Aosong Feng, Harshit Verma +7

Yale University · Arizona State University · University of Texas Rio Grande Valley

Time Series Reasoning RL for Language Model Reasoning Financial QA Time Series Forecasting Probabilistic Time Series Forecasting

May 21, 2026cs.LG

OPPO: Bayesian Value Recursion for Token-Level Credit Assignment in LLM Reasoning

Reinforcement learning with verifiable rewards has become the standard recipe for improving LLM reasoning, but the dominant algorithm GRPO assigns a single trajectory-level advantage to every token, diluting the signal at pivotal reasoning steps and injecting noise at uninformative ones. Critic-free alternatives derived from on-policy distillation supply per-token signals through oracle-conditioned likelihood ratios, yet apply each signal in isolation from the trajectory-level evidence accumulated up to that position. We propose Oracle-Prompted Policy Optimization (OPPO), which rests on a single observation: the oracle signal used by prior distillation-style methods for local discrimination is also the natural Bayesian update of the model's belief about eventual success. Accumulating the signal along a trajectory yields, in closed form and at the cost of one extra forward pass, a running estimate of the success probability at every position, together with a token-level advantage that requires no learned value network and no additional rollouts. A first-order analysis factorizes the advantage into the per-token discrimination signal used by distillation methods modulated by a state weight that concentrates credit on genuinely pivotal tokens, with a directional variance-reduction guarantee. The framework admits two estimators differing only in which model scores the evidence: a \textit{self-oracle} that reuses the student and recovers the on-policy distillation reward as a strict special case, and a \textit{teacher-oracle} that delegates scoring to a stronger frozen model. On two base LLMs across seven mathematics, science, and code reasoning benchmarks, OPPO improves over GRPO, DAPO, and SDPO by up to

+6.0

points on AMC'23 and

+5.2

points on AIME'24, with gains that widen monotonically with response length.

Yu Li, Rui Miao, Tian Lan +1

1George Washington University · 2The University of Texas at Dallas

Value Function Estimation Token-Level Credit Assignment RL for Language Model Reasoning Credit Assignment in RL Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards+3

May 20, 2026cs.LG

Why Semantic Entropy Fails: Geometry-Aware and Calibrated Uncertainty for Policy Optimization

Post-training has become central to improving reasoning and alignment in large language models, where critic-free models enable scalable learning from model-generated outputs but lack principled mechanisms to distinguish informative from noisy signals. Recent approaches leverage response-level measures as uncertainty signals to regulate group-based optimization methods such as GRPO. Yet their empirical success remains unstable and unclear in how they influence optimization dynamics. In this paper, we provide, to our knowledge, the first principled formulation that interprets uncertainty signals as mechanisms for characterizing and regulating gradient variance and learning signal quality. Based on both empirical and theoretical analysis, we identify two critical gaps of current entropy-based estimators: The anisotropic gap and The calibration gap. Motivated by this analysis, we propose Geometric-aware Calibrated Policy Optimization (GCPO), a novel framework integrating geometry-aware measures to capture semantic disagreement with reward-based calibration to align uncertainty with learning signal strength. Experiments on multiple benchmarks show that our approach more faithfully tracks gradient variability and consistently improves post-training performance. Our results highlight the importance of designing uncertainty signals that are aligned with optimization dynamics, offering a principled perspective for robust post-training.

Zheyuan Zhang, Kaiwen Shi, Han Bao +3

University of Notre Dame · †Corresponding Author

RL for Language Model Reasoning Policy Optimization Language Model Calibration Policy Gradient Methods LLM Uncertainty Estimation RL Post-Training

May 20, 2026cs.LG

You Only Need Minimal RLVR Training: Extrapolating LLMs via Rank-1 Trajectories

Reinforcement learning with verifiable rewards (RLVR) has become a dominant paradigm for improving reasoning in large language models (LLMs), yet the underlying geometry of the resulting parameter trajectories remains underexplored. In this work, we demonstrate that RLVR weight trajectories are extremely low-rank and highly predictable. Specifically, we find that the majority of downstream performance gains are captured by a rank-1 approximation of the parameter deltas, where the magnitude of this projection evolves near-linearly with training steps. Motivated by this, we propose a simple and compute-efficient method RELEX (REinforcement Learning EXtrapolation), which estimates the rank-1 subspace from a short observation window and extrapolates future checkpoints via linear regression, with no learned model required. Across three models (i.e., Qwen2.5-Math-1.5B, Qwen3-4B-Base, and Qwen3-8B-Base), RELEX produces checkpoints that match or exceed RLVR performance on both in-domain and out-of-domain benchmarks, requiring as few as 15% steps of full RLVR training. Remarkably, RELEX is able to extrapolate far beyond the observation window at no training cost, predicting checkpoints up to 10-20

\times

beyond the observed prefix with continued improvement (e.g., observe only the first 50 steps and extrapolate to 1000 steps). Our ablation analysis confirms the minimalist sufficiency of RELEX: neither increasing the subspace rank nor employing non-linear modeling yields further gains in extrapolation. Finally, we show that RELEX's success stems from a "denoising" effect: by projecting updates onto the rank-1 subspace, the model discards stochastic optimization noise that would otherwise degrade performance during extrapolation. Our code is available at https://github.com/weizhepei/RELEX.

Zhepei Wei, Xinyu Zhu, Wei-Lin Chen +3

University of Virginia · Washington University in St. Louis

RL for Language Model Reasoning Low-Rank Approximation Reinforcement Learning with Verifiable Rewards RL Post-Training

May 20, 2026cs.LG

DelTA: Discriminative Token Credit Assignment for Reinforcement Learning from Verifiable Rewards

Reinforcement learning from verifiable rewards (RLVR) has emerged as a central technique for improving the reasoning capabilities of large language models. Despite its effectiveness, how response-level rewards translate into token-level probability changes remains poorly understood. We introduce a discriminator view of RLVR updates, showing that the policy-gradient update direction implicitly acts as a linear discriminator over token-gradient vectors and thereby determines which token probabilities are increased or decreased during learning. Under standard sequence-level RLVR, this discriminator is constructed from positive- and negative-side centroids formed by advantage-weighted averaging of token-gradient vectors. However, such centroid construction can be dominated by shared high-frequency patterns, such as formatting tokens, diluting sparse yet discriminative directions that better distinguish high-reward responses from low-reward ones. To address this limitation, we propose

\textbf{DelTA}

, a discriminative token credit assignment method that estimates token coefficients to amplify side-specific token-gradient directions and downweight shared or weakly discriminative ones. These coefficients reweight a self-normalized RLVR surrogate, making the effective side-wise centroids more contrastive and thereby reshaping the RLVR update direction. On seven mathematical benchmarks, DelTA outperforms the strongest same-scale baselines by 3.26 and 2.62 average points on Qwen3-8B-Base and Qwen3-14B-Base, respectively. Additional results on code generation, a different backbone, and out-of-domain evaluations further demonstrate the generalization ability of DelTA.

Kaiyi Zhang, Wei Wu, Yankai Lin

Gaoling School of Artificial Intelligence, Renmin University of China · Ant International

Policy Gradient Token-Level Credit Assignment RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards

May 20, 2026cs.LG

How Much Online RL is Enough? Informative Rollouts for Offline Preference Optimization in RLVR

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for reasoning in language models, with GRPO as its primary example. However, GRPO requires continuous online rollout generation, making it computationally expensive and difficult to scale. While Direct Preference Optimization (DPO) offers a stable and efficient offline alternative, it is typically expected to underperform w.r.t. online RL methods such as GRPO when trained on rollouts from a cold supervised fine-tuned (SFT) policy. We introduce G2D (GRPO to DPO)}, a three-stage pipeline that performs a short GRPO warm-up, constructs a static preference dataset, and fine-tunes a model offline with DPO. Across a set of values of the number of online steps (K) in GRPO on Qwen2.5-7B and Llama-3.1-8B, we find that offline DPO with moderate warm-up matches or outperforms GRPO at substantially lower compute cost in our setting. On Qwen2.5-7B, G2D at K=150 achieves 62.4% on MATH-500, outperforming GRPO (51.6%) by 10.8% at ~4x lower compute. On Llama-3.1-8B, G2D at K=500 achieves 49.4%, surpassing GRPO in our experimental setting. We show that performance is not governed by the number of preference pairs, which does not vary much w.r.t. K, but by their informativeness. Moderate warm-up produces rollouts with calibrated uncertainty, yielding stronger contrastive signal, while excessive warm-up leads to overconfident policies and less informative data. Our results recast the offline-online gap in RLVR as primarily a data informativeness problem, and identify short online RL warm-up with appropriate difficulty calibration of the fine-tuning dataset as a compute-efficient alternative to online RL.

Richa Verma, Balaraman Ravindran

TCS Research Department of CSE IIT Madras Chennai, India · Department of Data Science & AI, Wadhwani School of Data Science & AI IIT Madras Chennai, India

Direct Preference Optimization RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Preference-Based RL

May 20, 2026cs.CL

LamPO: A Lambda Style Policy Optimization for Reasoning Language Models

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative objectives, such as GRPO, summarize each sampled group with scalar statistics and therefore discard fine-grained relational information among candidate responses. This weakens credit assignment under sparse outcome rewards, especially when multiple generated solutions differ only subtly in reasoning quality. We propose \textbf{LamPO}, a \textbf{Lambda-Style Policy Optimization} method that replaces scalar group advantages with a \emph{Pairwise Decomposed Advantage}. LamPO aggregates pairwise reward gaps within each response group and modulates each comparison by a confidence-aware weight computed from sequence log-probability differences, while retaining the critic-free and clipped-update structure of PPO-style optimization. When reference solutions are available, we further add a lightweight ROUGE-L-based dense auxiliary reward to reduce reward sparsity. Experiments on AIME24, AIME25, MATH-500, and GPQA-Diamond with Qwen3-1.7B, Qwen3-4B, and Phi-4-mini show that LamPO consistently improves over GRPO and recent RLVR variants, with more stable training dynamics and better sample efficiency.

Redacted by arXiv

Pinterest, San Francisco, CA 94107, USA

RL for Language Model Reasoning Group Relative Policy Optimization Policy Optimization Reinforcement Learning with Verifiable Rewards Sparse-Reward RL

May 20, 2026cs.LG

Advantage Collapse in Group Relative Policy Optimization: Diagnosis and Mitigation

Group Relative Policy Optimization (GRPO), a prominent algorithm within the Reinforcement Learning from Verifiable Rewards (RLVR) framework, has achieved strong results in improving the reasoning capabilities of large language models (LLMs). However, GRPO is prone to advantage collapse, a failure mode where homogeneous rewards within a group (e.g., all correct or all incorrect answers) yield near-zero advantages and vanishing gradients. To address this, we introduce the Advantage Collapse Rate (ACR), the first diagnostic metric quantifying the proportion of training batches with ineffective gradients. Across models from 0.5B to 14B parameters on mathematical reasoning benchmarks, we show that ACR strongly predicts training stagnation and final performance. We then propose Adaptive Virtual Sample Policy Optimization (AVSPO), a lightweight extension of GRPO that injects virtual reward samples, guided by real-time ACR monitoring, to enable learning from homogeneous groups without additional model rollouts. AVSPO reduces advantage collapse by 58-63% relative to GRPO and yields consistent accuracy gains of 4-6 percentage points across all model scales, while maintaining generalization on the evaluated out-of-domain task. Code and datasets are available at https://github.com/hexixiang/Advantage-Collapse-Rate.

Xixiang He, Qiyao Sun, Ao Cheng +5

National University of Defense Technology, Changsha, Hunan, China · Intelligent Game and Decision Lab, Beijing, China · The Chinese University of Hong Kong, Shenzhen, Guangdong, China

RL for Language Model Reasoning Group Relative Policy Optimization Policy Optimization Reinforcement Learning with Verifiable Rewards

May 20, 2026cs.CL

Thinking-while-speaking: A Controlled, Interleaved Reasoning Method for Real-Time Speech Generation

The thinking-while-speaking paradigm aims to make AI communication more human. A key challenge is maintaining fluent speech while performing deep reasoning. Our method, InterRS, tackles this by inserting reasoning steps only during natural speech generation. This requires high-quality data where reasoning and speech are precisely aligned, and the length ratio are under controlled. We introduce a novel pipeline to generate such seamlessly interleaved audio data. To train our model, we combine interleaved SFT with refined data and reinforcement learning with two new rewards: a TA-Balance Reward to manage timing and thinking-answer ratio, and a Linguistic Quality Reward to refine expression. Experiments show our approach achieves 13% better performance on mathmatical and logic benchmarks while generating instant response like a spoken-language instruct model which outputs fast CoT response. Furthermore, our method generates more natural and fluent answers than prior methods.

Xuan Du, Qiangyu Yan, Wenshuo Li +4

Huawei Technologies

RL for Language Model Reasoning Controllable Speech Generation Synthetic Data Generation for Language Models Speech Language Models

May 20, 2026cs.LG

Multi-Step Likelihood-Ratio Correction for Reinforcement Learning with Verifiable Rewards

Reinforcement learning with verifiable rewards (RLVR) plays a pivotal role in improving the reasoning ability of large language models. However, widely used PPO surrogate objectives are fundamentally local, as they rely on a local approximation of the exact policy gradient objective. While this approximation improves stability by reducing the variance induced by importance sampling, it also introduces structural bias into the surrogate objective, which must be controlled through trust region mechanisms. In this work, we introduce the

N

-step forward trace, which augments the PPO surrogate objective using the cumulative likelihood ratio of the next

N-1

tokens. Building on this idea, we propose

N

-Step Forward-Trace Policy Optimization (NFPO), a practical RLVR algorithm that integrates the

N

-step forward trace into the masked policy gradient framework. NFPO provides a continuous bridge between the PPO surrogate objective and the exact policy gradient objective, offering a principled mechanism for controlling the bias-variance trade-off. Our theoretical analysis shows that, with an appropriate choice of

N

, the proposed objective yields a tighter policy-improvement bound than the standard PPO surrogate. Experiments on comprehensive reasoning benchmarks demonstrate that NFPO consistently improves performance, supporting our theoretical findings.

Deokgyu Yoon, Hyungkyu Kang, Joongkyu Lee +4

1Seoul National University · 2Upstage

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Proximal Policy Optimization

May 20, 2026cs.LG

AGPO: Adaptive Group Policy Optimization with Dual Statistical Feedback

Reinforcement learning improves LLM reasoning, but PPO/GRPO typically use fixed clipping and decoding temperature, which makes training brittle and tuning-heavy. We propose Adaptive Group Policy Optimization (AGPO), a critic-free refinement of GRPO that uses group-level statistics to control both update magnitude and exploration. AGPO uses a shared probe-derived statistical state to drive two controllers: (i) adaptive clipping, which sets the trust-region size from reward dispersion and skewness, probe vote entropy, policy entropy, and step-wise KL drift; and (ii) bidirectional adaptive temperature sampling, which heats or cools decoding around a base temperature according to centered uncertainty relative to a running baseline. On nine English and Chinese math/STEM benchmarks, Qwen2.5-14B trained with AGPO outperforms PPO/GRPO under the same generated-token budget, reaching 67.3% on GSM8K and 40.5% on MATH. Gains transfer to Llama-3-8B and Gemma-2-9B, and ablations confirm both modules are complementary. Our implementation is publicly available at https://github.com/wandugu/paper_agpo.

Miaobo Hu, Shuhao Hu, Bokun Wang +5

Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100092, China · School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China · School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China

RL for Language Model Reasoning Group Relative Policy Optimization RL Fine-Tuning Policy Learning

May 19, 2026cs.AI

OSCToM: RL-Guided Adversarial Generation for High-Order Theory of Mind

Large Language Models (LLMs) perform well on many language tasks, but their Theory of Mind (ToM) reasoning is still uneven in complex social settings. Existing benchmarks, including ExploreToM, do not always test the recursive beliefs and information asymmetries that make these settings difficult. This paper presents OSCToM (Observer-Self Conflict Theory of Mind), an approach for modeling nested belief conflicts in LLM-based ToM tasks. The key case is one in which an observer's view of another agent conflicts with the observer's own belief state. Such cases go beyond simple perspective-taking and require recursive, multi-layered reasoning. OSCToM combines reinforcement learning (RL), an extended domain-specific language, and compositional surrogate models to generate observer-self conflicts. In our experiments, OSCToM-8B gives the best overall result among the systems tested. It improves on the reported ExploreToM results on FANToM and remains competitive on Hi-ToM and BigToM. On the information-asymmetric FANToM benchmark, OSCToM reaches 76% accuracy, compared with the 0.2% reported by ExploreToM. The data-synthesis procedure is also 6x more efficient, indicating that targeted training data can help smaller models handle advanced cognitive reasoning. The project code is available at https://github.com/sharminsrishty/osct.

Sharmin Sultana Srishty, Kazi Mahathir Rahman, Malaika Parizat Sakkhi +2

Department of Computer Science BRAC University

Cognitive Modeling Theory of Mind RL for Language Model Reasoning

May 19, 2026cs.AI

LC-ERD: Mining Latent Logic for Self-Evolving Reasoning via Consistency-Regulated Reward Decomposition

The evolution of Large Language Model (LLM) reasoning is bottlenecked by the scarcity of high-quality process data. While self-alignment via endogenous rewards offers a solution, mining valid supervision faces three challenges: (1) Label Noise via Mimetic Bias, where rewards prioritize statistical likelihood over logical truth, creating a "correctness illusion" that masks compounding errors; (2) Coarse-Grained Supervision, where sparse global outcomes (e.g., in GRPO) fail to provide granular guidance, treating reasoning chains as monolithic; and (3) Distributional Collapse, where signals fail to generalize without amplifying pre-training biases. To address these, we introduce LC-ERD (Logic-Consistent Endogenous Reward Decomposition), a framework framing self-alignment as latent structure mining. We derive a Variational Logic Potential by aggregating consensus from the model's Latent Logic Expertise (LLE) to denoise the reasoning manifold, and introduce a Multi-Agent Value Decomposition protocol based on the IGM principle to quantify individual step utility. Experiments show LC-ERD delivers a robust self-evolution path, uncovering trade-offs between logic consistency and accuracy while identifying high-value reasoning patterns missed by standard rewards. Our code is available at https://github.com/LC-ERD-repo/LC-ERD.

Yanyu Chen, Jiyue Jiang, Dianzhi Yu +8

The Chinese University of Hong Kong · Shanghai Jiaotong University · Fudan University

RL for Language Model Reasoning Process Supervision Language Model Self-Improvement

May 19, 2026cs.AI

Beyond Mode Collapse: Distribution Matching for Diverse Reasoning

On-policy reinforcement learning methods like GRPO suffer from mode collapse: they exhibit reduced solution diversity, concentrating probability mass on a single solution once discovered and ceasing exploration of alternative strategies. We show this stems from reverse KL minimization's mode-seeking behavior, which reinforces the first high-reward trajectory found rather than maintaining a distribution over multiple diverse solutions. We propose DMPO (Distribution-Matching Policy Optimization), which prevents mode collapse through principled approximation of forward KL minimization. DMPO constructs a group level target distribution over sampled trajectories proportional to their rewards, then aligns the policy distribution to this target. This provides mode-covering behavior without requiring sampling from the intractable global target distribution, enabling sustained exploration throughout training. We validate DMPO on NP-hard combinatorial optimization, where exponentially many feasible solutions exist but only a few approach optimality, an ideal testbed for evaluating exploration. DMPO achieves 43.9% Quality Ratio on text-based NP-Bench (vs. GRPO's 40.1%) and 43.1% on vision-based NP-Bench (vs. 38.4%), demonstrating 9% and 12% relative improvements respectively. These gains generalize to mathematical reasoning (+2.0%) and out-of-domain tasks (+2.3%), showing that diversity-preserving training enhances general reasoning capabilities across modalities. Our work establishes distribution matching as a practical, principled approach to preventing mode collapse in on-policy RL, with consistent quality improvements demonstrating sustained exploration across diverse reasoning tasks.

Xiaozhe Li, Yang Li, Xinyu Fang +10

1Tongji University, China · 6Independent · 2Shanghai AI Laboratory, China +3

KL-Regularized RL RL for Language Model Reasoning RL Exploration Mode Collapse

May 19, 2026cs.LG

Detecting and Mitigating the Correct-Answer Extinction Window in Test-Time Reinforcement Learning with Majority Voting

Test-time reinforcement learning (TTRL) reports substantial accuracy gains on mathematical reasoning benchmarks using majority vote as a pseudo-label signal. We argue these gains are systematically misinterpreted: most reflect sharpening of already-solvable problems rather than genuine learning, while problems corrupted from correct to incorrect outnumber truly learned ones, and this damage is irreversible once majority vote locks onto a wrong answer. Per-problem tracking reveals that correct-answer signals in low-ability problems are briefly active before being permanently suppressed, a phenomenon we term the \textit{Correct-Answer Extinction Window}, with Flip Rate (FR) as its leading indicator. We thus propose TTRL-Guard, a lightweight framework with three mechanisms targeting the extinction window: Flip-Rate-Aware Reward Scaling (FRS) down-weights at-risk updates as FR declines, Minority-Preserving Sampling (MPS) retains gradient signal from minority correct answers, and Risk-Conditioned Sparse Updatings (RCSU) suspends updates on polarized problems. Experiments across three models and four benchmarks show that TTRL-Guard achieves the best average pass@1 on Qwen2.5-7B-Instruct and Qwen3-4B, improves relatively over TTRL by +54% on AIME 2025.

Hongxiang Lin, Zhirui Kuai, Erpeng Xue +1

Meituan

Reinforcement Learning RL for Language Model Reasoning Mathematical Reasoning Test-Time RL Majority Voting

May 19, 2026cs.LG

CEPO: RLVR Self-Distillation using Contrastive Evidence Policy Optimization

When a model produces a correct solution under reinforcement learning with verifiable rewards (RLVR), every token receives the same reward signal regardless of whether it was a decisive reasoning step or a grammatical filler. A natural fix is to condition the model on the correct answer as a teacher, identifying tokens it would have generated differently had it known the answer. Prior work shows this either corrupts training by leaking the answer into the gradient, or produces a weak signal that cannot distinguish decisive steps from filler, since both look equally surprising relative to the model's baseline. We propose Contrastive Evidence Policy Optimization (CEPO), which asks a sharper question at every token: not just "does the correct answer favor this token?" but "does the correct answer favor it while the wrong answer disfavors it?" A token satisfying both is a genuine reasoning step; one satisfying neither is filler. The wrong-answer teacher is constructed from rejected rollouts already in the training batch, incurring no additional sampling cost. We prove CEPO inherits all structural safety guarantees of the prior state of the art while strictly sharpening credit at decisive tokens, with the improvement vanishing exactly at filler positions. Empirically, CEPO achieves 43.43% and 60.56% average accuracy across five multimodal mathematical reasoning benchmarks at 2B and 4B scale, respectively, versus 41.17% and 57.43% for GRPO under identical training budgets. Distribution-matching self-distillation methods (OPSD, SDPO) fall below the untrained baseline, empirically confirming the information leakage our theory predicts. Our code is available at https://github.com/ahmedheakl/CEPO.

Ahmed Heakl, Abdelrahman M. Shaker, Youssef Mohamed +4

MBZUAI · Linköping University · Australian National University

Token-Level Credit Assignment RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards On-Policy Distillation Knowledge Distillation

May 19, 2026cs.LG

When to Stop Reusing: Dynamic Gradient Gating for Sample-Efficient RLVR

Reinforcement Learning with Verifiable Rewards (RLVR) has become the dominant paradigm for advanced reasoning in Large Language Models (LLMs), but rollout samples are expensive to obtain, making sample efficiency a critical bottleneck. A natural remedy is to reuse each rollout batch for multiple gradient updates, a standard practice in classical RL. Yet in RLVR, this amplifies policy shift, leading to severe performance degradation. Detecting the onset of degradation early enough to stop reuse remains an open and challenging problem. We close this gap by identifying the \textit{Disproportionate Weight Divergence (DWD)} phenomenon: performance degradation is synchronized with a sharp surge in the \texttt{lm_head} weight change, while intermediate layers remain stable. Empirically, we verify that DWD emerges consistently across diverse LLMs and tasks. Theoretically, we prove that (i) harmful gradients concentrate at the \texttt{lm_head} while intermediate layers are structurally attenuated, and (ii) the \texttt{lm_head} gradient norm lower-bounds the policy divergence. These results establish the \texttt{lm_head} gradient norm as a principled, real-time signal of catastrophic policy shift. Guided by this insight, we propose \textit{Dynamic Gradient Gating (DGG)}, a lightweight intervention that monitors the \texttt{lm_head} gradient norm in real time and intercepts harmful gradients before they corrupt the optimizer. DGG consistently matches or exceeds the standard single-use baseline, achieving up to

2.93\times

sample efficiency and

2.14\times

wall-clock speedup across math, ALFWorld, WebShop, and search-augmented QA tasks.

Yuchun Miao, Sen Zhang, Yuqi Zhang +4

National Engineering Research Center for Multimedia Software, School of Computer Science, Wuhan University · Meituan Longcat Team · The University of Sydney +1

RL for Language Model Reasoning Policy Optimization Reinforcement Learning with Verifiable Rewards Sample-Efficient RL

May 19, 2026cs.CL

LambdaPO: A Lambda Style Policy Optimization for Reasoning Language Models

Group Relative Policy Optimization(GRPO) has become a cornerstone of modern reinforcement learning alignment, prized for its efficacy in foregoing an explicit value-critic by leveraging reward normalization across sampled trajectory cohorts. However, the method's reliance on a monolithic statistical baseline, such as the group mean, collapses the relational topology of the trajectory space into a single scalar, thereby erasing the fine-grained preference information essential for navigating complex, rank-sensitive reward landscapes. To address this issue, we introduce a novel framework, Lambda Policy Optimization (LambdaPO), that addresses this information-theoretic bottleneck by re-conceptualizing advantage estimation from a scalar value to a decomposed, pairwise preference structure. Specifically, the advantage for any given trajectory is formulated as the integrated sum of reward differentials against all peers in its cohort, where each pairwise comparison is dynamically attenuated by the policy's own probabilistic confidence in the established preference. To further mitigate the sparsity of binary outcome supervision, we augment the objective with a semantic density reward, derived from the precision-recall alignment between generated reasoning traces and ground-truth solutions. As a result, our method can mine more fine-grained optimization signals from a group of rollouts, guiding the LLM to a better optima. Experimental results across challenging math reasoning and question-answering tasks demonstrates that LambdaPO improves performance compared to the baseline methods.

Redacted by arXiv

RL for Language Model Reasoning Group Relative Policy Optimization Preference-Based RL

May 19, 2026cs.CL

Taming the Thinker: Conditional Entropy Shaping for Adaptive LLM Reasoning

Entropy-based deep reasoning has emerged as a promising direction for improving the reasoning capabilities of Large Language Models (LLMs), but existing methods often either increase response length indiscriminately or shorten responses at the cost of accuracy. To better balance this trade-off, we introduce Conditional Entropy Shaping (CES), a framework that dynamically controls token-level response entropy, enabling LLMs to produce concise solutions on simple problems while encouraging deeper exploration on hard ones. Built on DAPO, CES uses token-level entropy as an uncertainty signal and applies a conditional bidirectional policy: it penalizes high-entropy "forking point" tokens on correct reasoning paths to improve conciseness, and rewards them on incorrect paths to encourage exploration and error correction. We implement CES on DeepSeek-R1-Distill-7B and evaluate it on 12 mathematical benchmarks. CES consistently improves average accuracy while reducing response length relative to DAPO, and supplementary experiments show similar trends on a smaller 1.5B backbone and on out-of-domain benchmarks.

Shuyu Wei, Jian Sun, Delai Qiu +6

Beijing Key Laboratory of Traffic Data Mining and Embodied Intelligence, Beijing Jiaotong University · Unisound AI Technology Co., Ltd.

RL for Language Model Reasoning LLM Reasoning Large Reasoning Models

May 18, 2026cs.AI

AMR-SD: Asymmetric Meta-Reflective Self-Distillation for Token-Level Credit Assignment

The alignment of Large Language Models (LLMs) for complex reasoning heavily relies on Reinforcement Learning with Verifiable Rewards (RLVR). However, standard algorithms like GRPO apply sequence-level rewards uniformly to all tokens, creating a severe credit-assignment bottleneck. While on-policy self-distillation attempts to resolve this by conditioning a self-teacher on privileged contexts, direct exposure to raw oracle solutions often induces over-conditioned teacher distributions, implicit answer leakage, and late-stage training collapse. To overcome these limitations, we propose Asymmetric Meta-Reflective Self-Distillation (AMR-SD). Instead of conditioning directly on raw reference traces, AMR-SD inserts a reflection bottleneck: it compresses diagnostic signals -- from verifier outcomes, peer rollouts, or reference feedback -- into concise, self-generated Socratic hints and critiques. Furthermore, we introduce Causal Information Gain (CIG) with an asymmetric, ReLU-gated threshold to translate these reflections into sparse, highly precise token-level advantage modulations. Combined with temporal annealing, this mechanism preserves the base environmental reward while filtering out distributional noise. Experiments across scientific, mathematical, and tool-use benchmarks demonstrate that AMR-SD significantly outperforms existing baselines, achieving robust long-horizon stability and successfully preventing late-stage collapse.

Zhenlin Wei, Pu Jian, Yingzhuo Deng +6

Meituan Beijing, China · University of Chinese Academy of Sciences

Token-Level Credit Assignment RL for Language Model Reasoning Step-Level Credit Assignment in RL Language Model Distillation Reinforcement Learning with Verifiable Rewards

May 18, 2026cs.CL

Implicit Hierarchical GRPO: Decoupling Tool Invocation from Execution for Tool-Integrated Mathematical Reasoning

Large language models (LLMs) have increasingly leveraged tool invocation to enhance their reasoning capabilities. However, existing approaches typically tightly couple tool invocation with immediate execution. Such immediate tool interaction may disrupt the reasoning coherence of LLMs and constrain their expressivity, ultimately degrading reasoning performance. To this end, for the first time, we propose and formalize the problem of decoupling tool invocation from execution during reasoning, and introduce delayed execution with explicit control to enhance tool-integrated reasoning (TIR). Furthermore, we propose a hierarchical control framework and theoretically derive a surrogate loss that enables an implicitly hierarchical policy to learn behavior equivalent to that of an explicit hierarchical policy, leading to the proposed IH-GRPO algorithm. Extensive experiments on IH-GRPO achieve absolute improvements of 1.87%, 2.16%, and 2.53% on Qwen3-1.7B, Qwen3-4B, and Qwen3-8B across six out-of-domain mathematical reasoning benchmarks over the strongest baseline method, while also yielding consistent performance gains in other domains. Our code is available at https://github.com/Lumina04/IH-GRPO-01.

Li Wang, Xiaohan Wang, Xiaodong Lu +5

Meituan · Tsinghua University

RL for Language Model Reasoning Hierarchical RL LLM Tool Use LLM Mathematical Reasoning RL for Tool Use

May 18, 2026cs.LG

FBOS-RL: Feedback-Driven Bi-Objective Synergistic Reinforcement Learning

Reinforcement learning has become a cornerstone for aligning and unlocking the reasoning capabilities of large-scale models. At its core, the training loop of GRPO and its variants alternates between rollout sampling and policy update: the policy first samples rollouts from its action space, and then updates its parameters according to the advantages computed over them. Unlike supervised learning, where each gradient step is anchored to an explicit ground-truth target, the optimal gradient direction for updating model parameters in this setting is not known a priori; the high-quality rollouts drawn during the sampling stage therefore act as the implicit "teacher" that guides every parameter update. However, mainstream RL algorithms such as GRPO adopt a simple sampling scheme that conditions all rollouts on the same original prompt. When a task lies beyond the policy model's current capability, this sampling scheme rarely yields a high-quality rollout, leaving the policy model without a meaningful gradient direction when updating its parameters, which causes training to stall. To address this issue, we propose FBOS-RL. Specifically, we let the model perform Feedback-Guided Exploration Enhancement based on the feedback provided by the environment, and on top of this we design two mutually reinforcing training objectives: EPA and ECC. Extensive experiments demonstrate that EPA and ECC can mutually reinforce each other, forming a positive flywheel effect that significantly improves both the training efficiency and the final performance ceiling of reinforcement learning. Specifically, under both an identical number of rollouts and the same number of training steps, FBOS-RL learns substantially faster than GRPO and feedback-based baselines and ultimately attains a higher performance ceiling, while exhibiting higher policy entropy and lower gradient norms throughout training.

Xikai Zhang, Yongzhi Li, Likang Xiao +6

Hangzhou International Innovation Institute, Beihang University · Kuaishou Technology · School of Artificial Intelligence, Beihang University

RL for Language Model Reasoning RL Exploration RL Post-Training RL Fine-Tuning

May 18, 2026cs.AI

SD-Search: On-Policy Hindsight Self-Distillation for Search-Augmented Reasoning

Search-augmented reasoning agents interleave internal reasoning with calls to an external retriever, and their performance relies on the quality of each issued query. However, under outcome-reward reinforcement learning, every search decision in a rollout shares the same trajectory-level reward, leaving individual queries without step-specific credit. Recent process-supervision approaches address this gap by drawing step-level signals from outside the policy, relying either on a much larger teacher model, or on sub-question annotations produced by a stronger external system. In contrast, we propose SD-Search, which derives step-level supervision from the policy itself through on-policy hindsight self-distillation, requiring neither an external teacher nor additional annotations. In SD-Search, a single model plays two roles that differ only in conditioning: a student that sees only the context available at inference time, and a teacher that additionally conditions on a compact hindsight block summarizing the search queries and final outcomes of a group of rollouts sampled from the same question. Since the teacher knows how each rollout unfolded and which ones succeeded, its query distribution implicitly marks which decisions were worth making, and the student is trained to recover this behavior by minimizing the token-level Jensen--Shannon divergence to the teacher at search-query positions. This layers a dense, step-level signal on top of GRPO's coarse trajectory reward. Crucially, this signal is produced by the policy itself within the standard RL training loop, without external model inference, auxiliary annotation pipeline, or additional training stage.

Yufei Ma, Zihan Liang, Ben Chen +6

Kuaishou Technology

On-Policy Self-Distillation RL for Language Model Reasoning Agentic RAG RL Post-Training LLM Reasoning

May 18, 2026cs.CL

Knowledge-to-Verification: Exploring RLVR for LLMs in Knowledge-Intensive Domains

Reinforcement learning with verifiable rewards (RLVR) has demonstrated promising potential to enhance the reasoning capabilities of large language models (LLMs) in domains such as mathematics and coding. However, its applications on knowledge-intensive domains have not been effectively explored due to the scarcity of high-quality verifiable data. Furthermore, current RLVR focuses solely on the correctness of final answers, leading to the limitations of flawed reasoning and sparse reward signals. In this work, we propose Knowledge-to-Verification (K2V), a framework that extends RLVR to knowledge-intensive domains through automated verifiable data synthesis, while enabling verification of the LLM's reasoning process. Extensive experiments demonstrate that K2V enhances the reasoning of LLM in knowledge-intensive domains without significantly compromising the model's general capabilities. This study also suggests that integrating automated data synthesis with reasoning verification is a promising direction to enhance model capabilities in these broader domains. Code is available at https://github.com/SeedScientist/K2V.

Zhonghang Yuan, Zhefan Wang, Fang Hu +7

Shanghai Artificial Intelligence Laboratory · Shanghai Innovation Institute

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Reasoning Verification