Reinforcement Learning with Verifiable Rewards

Also known as RLVR

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59 papers in the last four weeks, up 119% on the four weeks before. 0.6% of all new papers.

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Jun 10, 2026cs.CL

Verifiable Environments Are LEGO Bricks: Recursive Composition for Reasoning Generalization

Reinforcement Learning (RL) with verifiable environments has emerged as a powerful approach for enhancing the reasoning capabilities of Large Language Models (LLMs). While prior research demonstrates that scaling environment quantity improves RL performance, existing manual or individual construction methods suffer from linear scaling limits, thereby hindering scalable reasoning generalization. This paper introduces RACES (\textbf{R}ecursive \textbf{A}utomated \textbf{C}omposition for \textbf{E}nvironment \textbf{S}caling), a framework that conceptualizes verifiable environments as composable building blocks that can be recursively assembled. The key insight is that when the codomain (output type) of one environment matches the domain (input type) of another, they can be automatically fused into a new verifiable environment, enabling recursive composition. RACES is implemented with 300 individual environments and defines a set of composition operators (\textsc{SEQUENTIAL}, \textsc{PARALLEL}, \textsc{SORT}, and \textsc{SELECT}) that induce diverse reasoning patterns. Extensive experiments show that RL training on these composite environments consistently enhances reasoning generalization. Specifically, RACES improves DeepSeek-R1-Distill-Qwen-14B by an average of 3.1 points (from 48.2 to 51.3) and boosts Qwen3-14B performance from 58.8 to 61.1 on six benchmarks, which are unseen during the construction of training environments. Moreover, RACES achieves performance comparable to training on 300 individual environments using only 50 base environments, demonstrating significant efficiency in environment utilization.

Hao Xiang, Qiaoyu Tang, Le Yu +8

University of Chinese Academy of Sciences · Chinese Information Processing Laboratory, Institute of Software, Chinese Academy of Sciences · Qwen Team, Alibaba Group

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Procedural Content Generation

Jun 10, 2026cs.AI

SVoT: State-aware Visualization-of-Thought for Spatial Reasoning via Reinforcement Learning

Spatial reasoning remains a challenge for Multimodal Large Language Models (MLLMs), as it requires reliable multi-hop inference over both intermediate states and state transitions. Current studies often leave intermediate states unverified and treat state transitions as implicit processes, which limits reliability in multi-hop spatial reasoning. To address this, we propose State-aware Visualization-of-Thought (SVoT), a reinforcement learning framework that generates interleaved, verifiable intermediate states and visualizations. SVoT integrates transition reasoning chains into the generation processes, enabling the model to verify action preconditions and effects through interleaved textual and visual reasoning. We train SVoT via Group Relative Policy Optimization (GRPO), instantiating verification through reward design and evaluating the efficacy of different fine-grained rewards. As existing benchmarks reduce state transitions to single-variable updates, substantially simplifying the problems, we establish five domains by extending classical environments and introducing two novel domains, Pacman and Gather, that require multi-object interactions and numerical reasoning. These domains support systematic evaluation of multi-hop spatial reasoning with quantitative verification of generated intermediate states and transition reasoning. SVoT with transition-aware supervision achieves state-of-the-art performance across the introduced domains, yielding up to a 65% absolute accuracy gain on out-of-distribution test sets.

Chao Lei, Yanbei Jiang, Markus Hiller +4

School of Computing and Information Systems The University of Melbourne Melbourne, Australia

Visual Spatial Reasoning Reinforcement Learning with Verifiable Rewards Multimodal CoT Reasoning Visual CoT RL for VLMs

Jun 9, 2026cs.LG

TRACE: A Unified Rollout Budget Allocation Framework for Efficient Agentic Reinforcement Learning

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for enhancing reasoning and agentic behavior in large language models. However, rollout-intensive policy optimization is often limited by insufficient reward contrast, arising when overly simple or complex prompts generate low-variance feedback and when outcome-only rewards assign the same terminal assessment to every decision in a multi-turn rollout. Past efforts have focused on allocating available rollout resources to promising prompts, yet they only leverage sample informativeness at the prompt level and neglect variation in prefix-level informativeness across turns within the same rollout. This work targets multi-turn agentic RL by modeling each ReAct-style thought-action-observation turn as a semantically distinct node, allowing budget allocation to extend from prompt roots to turn-level prefixes with further continuations, which naturally forms tree-structured rollouts. We introduce Tree Rollout Allocation for Contrastive Exploration (TRACE), a unified rollout allocation framework that enhances reward contrast within a fixed sampling budget. Technically, TRACE allocates rollout budget to both prompt roots and intermediate prefixes that are most likely to yield mixed terminal rewards. A shared generalizable predictor estimates conditional success probability at these anchors from prefix histories to guide this allocation. The resulting adaptive tree structure enriches outcome-only feedback and amplifies the policy-update signal. Empirically, TRACE achieves competitive performance and efficiency gains on typical agentic benchmarks, e.g., improving Qwen3-14B Multi-Hop QA average accuracy by 2.8 points over competitive baselines at equal sampling cost.

Heming Zou, Qi Wang, Yun Qu +9

1Tsinghua University · 2LLM Department, Tencent

Agentic RL Reinforcement Learning with Verifiable Rewards Sample-Efficient RL

Jun 9, 2026cs.LG

Beyond Uniform Token-Level Trust Region in LLM Reinforcement Learning

Reinforcement learning with verifiable rewards (RLVR) has become standard for improving LLM reasoning. However, existing PPO-style trust-region mechanisms remain position-agnostic by enforcing uniform thresholds across all tokens independently. This pointwise treatment conflicts with autoregressive generation in two critical ways. First, uniform thresholds ignore autoregressive asymmetry. Early-stage deviations produce compounding sequence-level drift, causing static thresholds to under-regulate early divergence and excessively constrain late-stage exploration. Second, evaluating token-level divergence in isolation overlooks cumulative prefix drift, granting the same divergence allowance regardless of how far the conditioning history has already deviated from the rollout policy. To address this limitation, we propose CPPO (Cumulative Prefix-divergence Policy Optimization), a token-level masking rule that aligns updates with a finite-horizon policy-improvement bound via two coupled mechanisms. First, a position-weighted threshold imposes stricter limits at early positions whose effects persist longer, relaxing constraints for late-stage tokens. Second, a cumulative prefix budget tracks historical deviations, dynamically restricting further token-level deviation to prevent compounding errors along the prefix. Empirically, CPPO enhances training stability and significantly improves reasoning accuracy across various model scales.

Renjie Mao, Xiangxin Zhou, Lvfang Tao +7

Tencent Hunyuan

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

Jun 9, 2026cs.IR

Effective Reinforcement Learning for Agentic Search by Recycling Zero-Variance Queries During Training

The use of GRPO-style algorithms has become the standard strategy for training LLM search agents under outcome-only rewards. With these algorithms, a query contributes to parameter updates only when its rollout group mixes successes and failures; all-correct (too-easy) and all-incorrect (too-hard) groups are zero-variance and waste rollout cost. Existing approaches treat zero-variance as a static property and either discard or pre-filter such groups. We hypothesize and empirically validate that queries flip between zero-variance and signal-bearing states as the policy evolves during training. Building on this intuition, we propose query recycling, which returns zero-variance groups to a mutable pool for future resampling, so that the effective training distribution co-evolves with the policy. With the proposed technique, a 1.7B parameter model trained on synthetic data can reach 66.0 average Pass@1 accross seven multi-hop QA benchmarks, matching or surpassing systems with up to 7B parameters trained on benchmark-derived supervision. Analysis of recycling patterns shows that recycled queries supply roughly three quarters of the effective batch by the end of training, with contributions split between recovery from policy improvement and policy drift.

João Coelho, João Magalhães, Bruno Martins +1

Language Technologies Institute, Carnegie Mellon University, United States · Instituto Superior Técnico and INESC-ID, University of Lisbon, Portugal · NOVA LINCS, NOVA School of Science and Technology, Portugal

Reinforcement Learning Group Relative Policy Optimization Reinforcement Learning with Verifiable Rewards Policy Learning RL for LLM Agents

Jun 8, 2026cs.AI

Proxy Reward Internalization and Mechanistic Exploitation: A Learned Precursor to Reward Hacking and Its Generalization

Reward hacking is usually studied after it becomes visible, once a model earns high proxy reward while failing the intended task. We instead study what proxy RL teaches before that failure appears. We introduce Proxy Reward Internalization and Mechanistic Exploitation (PRIME), a learned capability to assess task correctness, predict proxy acceptance, and reason about exploitable proxy--gold gaps. In coding RL environments with exploitable pytest rewards, we measure PRIME through chain-of-thought monitoring, direct probes, and activation-level concept vectors. We find that PRIME emerges in a staged sequence before sustained reward hacking, and that its current direct-probe score forecasts later hack onset and severity even when the visible hack rate is still low. PRIME also adapts when the evaluator changes, retargeting to whichever proxy--gold gap remains rewarded and persisting when gold reward suppresses overt hacking, and ablating its activation directions reduces hacking. Across checkpoints, in-domain PRIME tracks out-of-domain misalignment. Together these results suggest that exploitable proxy RL amplifies a proxy-internalization capability upstream of visible hacking, making PRIME a candidate early-warning signal for broader alignment risk.

Mohammad Beigi, Ming Jin, Lifu Huang

1UC Davis · 2Virginia Tech

Reward Hacking Reinforcement Learning with Verifiable Rewards

Jun 8, 2026cs.CV

CapRL++: Unified Reinforcement Learning with Verifiable Rewards for Dense Image and Video Captioning

Image and video captioning are fundamental tasks that bridge the visual and linguistic domains, playing a critical role in pre-training Large Vision-Language Models (LVLMs). Current state-of-the-art captioning models are typically trained with Supervised Fine-Tuning (SFT), a paradigm that relies on expensive, non-scalable annotations and often causes models to memorize specific ground-truth answers, limiting their generality and ability to generate diverse, creative descriptions. To overcome these limitations, we propose applying Reinforcement Learning with Verifiable Rewards (RLVR) to the open-ended task of multimodal captioning. We introduce Captioning Reinforcement Learning++ (CapRL++), a novel reference-free training framework that redefines caption quality through its utility: a high-quality caption should enable a non-visual language model to accurately answer questions about the corresponding visual content. CapRL++ employs a decoupled two-stage pipeline where an LVLM generates a caption, and the objective reward is derived from the accuracy of a separate, vision-free LLM answering Multiple-Choice Questions based solely on that caption. Evaluations on more than 20 image and video benchmarks show that CapRL++ improves dense caption quality and strengthens caption-based pretraining across tasks such as spatial and temporal understanding. Pretraining on scalable image and video caption datasets annotated by CapRL++ yields substantial downstream gains. Furthermore, within the Prism Framework for caption quality evaluation, compact models trained with CapRL++ achieve dense captioning performance comparable to substantially larger models such as Qwen2.5-VL-72B and Qwen3-VL-235B-A22B. These results validate that CapRL++ effectively trains models to produce generalizable, high-fidelity descriptions, establishing a robust foundation beyond the limitations of traditional SFT.

Penghui Yang, Long Xing, Xiaoyi Dong +10

Tsinghua University · University of Science and Technology of China · Microsoft +4

Image Captioning Multimodal Pretraining Video Captioning Reinforcement Learning with Verifiable Rewards RL for VLMs

Jun 8, 2026cs.LG

Reasoning Arena: Trace Tournaments When Verifiable Rewards Fall Short

Reinforcement learning with verifiable rewards (RLVR) has become a leading paradigm for improving the reasoning ability of large language models through outcome-based supervision. However, verifiable rewards frequently become uninformative at the group level: when all sampled traces of a given prompt receive identical rewards, group-relative advantage estimation provides no gradient signal, even though the traces may differ substantially in reasoning quality. We propose Reasoning Arena, an adaptive training framework that routes such non-diverse reward groups to a judge system instead of discarding them. Beyond examining the final answer, Reasoning Arena constructs trace tournaments, where reasoning traces are compared head-to-head to expose finer-grained preferences within the group, converting reasoning quality into rich relative reward signals. To make reward estimation efficient, rather than exhaustively comparing every pair, each new trace is evaluated against a small, dynamically updated pool of previously generated traces as anchors to efficiently establish a relative ranking. We then fit a Bradley-Terry model on the incomplete comparison graph, enabling scalable RL integration without quadratic pairwise comparisons. Empirical results demonstrate that Reasoning Arena consistently outperforms the RLVR baseline by 7.6% on average in competition mathematics and coding benchmarks. By converting otherwise wasted zero-advantage samples into useful gradient updates, our method accelerates training by 27% to 41%, saving nearly 50% of generation compute, and substantially improves overall reasoning performance.

Han Zhou, Adam X. Yang, Laurence Aitchison +2

University of Cambridge · 2Mistral AI · *Work done as an AI Scientist Intern at Mistral AI.

Pairwise Preference Learning Reward Modeling RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Bradley–Terry Model Reward Design for RL+1

Jun 8, 2026cs.LG

PBSD: Privileged Bayesian Self-Distillation for Long-Horizon Credit Assignment

Long-horizon agentic tasks pose a fundamental credit assignment challenge for outcome-base reinforcement learning: trajectory-level rewards verify final correctness but provide limited guidance on which intermediate reasoning steps or tool interactions contribute to the outcome. The difficulty is especially pronounced in multi-turn search agents, where successful trajectories may contain misleading actions and failed trajectories may contain valuable evidence-gathering steps. We propose PBSD (Privileged Bayesian Self-Distillation), a Bayes-calibrated self-distillation method for fine-grained credit assignment under sparse final rewards. PBSD measures trajectory quality through the posterior-to-prior probability ratio of the verified answer and applies Bayes' rule to convert this hard-to-estimate answer-side ratio into a tractable likelihood ratio between a standard student model and a privileged answer-conditioned teacher model. Autoregressive decomposition of this Bayesian evidence score yields turn-level signals that identify whether each intermediate turn supports or undermines the verified outcome. Consequently, PBSD provides a principled and elegant reweighting scheme that transforms sparse outcome supervision into Bayes-calibrated turn-level credit signals, while remaining fully compatible with standard policy optimization. Experiments demonstrate that PBSD consistently enhances performance across both in-domain and out-of-domain settings, and effectively transfers knowledge from short-context training to long-context inference, suggesting that its fine-grained credit assignment mechanism facilitates more effective policy learning and yields improved generalization.

Yang Tian, Rui Wang, Xumeng Wen +5

School of AI, Shanghai Jiao Tong University · 2XYZ AI Lab

Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Step-Level Credit Assignment Self-Distillation Sparse-Reward RL Policy Learning+1

Jun 8, 2026cs.AI

ComplexConstraints and Beyond: Expert Rubrics for RLVR

Evaluation protocols can lag behind LLM capabilities. Programmatically verified benchmarks cover narrow surface constraints, whereas real-world instruction following and agentic workflows require judging semantic, contextual, and policy-dependent behavior. We study expert-curated rubric-based evaluation as a unified mechanism for measurement and reinforcement-learning rewards across two settings: complex instruction following and enterprise agentic tasks. We identify rubric-design choices that affect reward quality, including maximum viable atomicity, intent-aware criterion design, and LLM-judge calibration. We introduce ComplexConstraints, an expert-curated instruction-following suite comprising a public 75-prompt benchmark with 1,559 rubric criteria and a disjoint 1,000-prompt training set, with 10-40 atomic criteria per prompt. Empirically, rubric rewards improve training in both fixed task datasets, such as ComplexConstraints, and stateful RL environments, such as CoreCraft. Training a 4B model on ComplexConstraints improves mean criterion pass rate by +15.5 pp on a held-out split, bringing it within 0.5 pp of the untrained baseline of a roughly 60x larger Qwen3 model, and the gains transfer to external benchmarks the model never saw during training: +8.4 pp on AdvancedIF and +10.1 pp on MultiChallenge. In CoreCraft, rubric-reward RL likewise transfers to out-of-distribution benchmarks (+4.5 pp BFCL, +7.4 pp tau^2-Bench, +6.8 pp Toolathlon). These results show that expert-authored rubrics provide effective evaluation targets and scalable reward signals for improving LLM instruction following and agentic behavior.

Sushant Mehta, Liudas Panavas, Suhaas Garre +1

Surge AI

LLM-as-a-Judge Rubric-Based RL Instruction Following Reinforcement Learning with Verifiable Rewards LLM Agent Training Rubric-Based Evaluation+1

Jun 7, 2026cs.LG

sGPO: Trading Inference FLOPs for Training Efficiency in RLVR

Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.

Shivchander Sudalairaj, Kai Xu, Akash Srivastava +1

AI Innovation, Red Hat · Core AI, IBM

Group Relative Policy Optimization Adaptive Sampling Reinforcement Learning with Verifiable Rewards Sample-Efficient RL

Jun 7, 2026cs.AI

Momentum for Reasoning: Dense Intrinsic Signals in Policy Optimization

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for eliciting long-chain reasoning in large language models. However, existing methods based on Group Relative Policy Optimization (GRPO) rely on a binary outcome reward, which induces two structural failure modes: Zero-Advantage Collapse, in which all rollouts in a group share the same outcome and the gradient vanishes, and Hallucinated Certainty, in which the model becomes increasingly confident on incorrect rollouts late in training. We address both modes by densifying the reward with intrinsic signals computed entirely from the policy's own conditional probabilities, and propose ISPO (Intrinsic Signal Policy Optimization, which combines a sequence-level signal measuring how informative the thinking trajectory is for the final answer, with a token-level directional reward whose hallucinated-certainty hinge penalizes confidently-wrong predictions at critical decision tokens. Across three base models and five mathematical reasoning benchmarks, ISPO consistently outperforms competitive baselines, with the largest gains on the hardest benchmarks where zero-advantage collapse is most frequent, and training-dynamics diagnostics confirm that both failure modes are decreased.

Hao Chen, Zhanming Shen, Liyao Li +8

Zhejiang University · The Chinese University of Hong Kong · Eastern Institute of Technology

Intrinsic Reward Methods Reinforcement Learning RL for Language Model Reasoning Group Relative Policy Optimization Dense Reward RL Mathematical Reasoning+3

Jun 7, 2026cs.AI

Towards Long-Horizon Vessel Trajectory and Destination Forecasting with Reasoning Large Language Models

Long-horizon maritime trajectory prediction is important for shipping management, logistics planning, and maritime risk analysis, yet month-level forecasting remains insufficiently studied. Existing deep learning methods mainly focus on short- and mid-term coordinate extrapolation and often struggle to preserve route feasibility and destination correctness over extended horizons. This paper investigates joint long-horizon vessel trajectory and destination forecasting with reasoning-capable large language models, and develops a Maritime LLM post-training framework based on Reinforcement Learning with Verifiable Reward (RLVR). An AIS-based benchmark is constructed with 60-day historical trajectories and 30-day forecasting horizons, where trajectories are converted into semantic textual representations for RL prompt construction. RLVR aligns LLMs with maritime forecasting objectives by enforcing physical validity, providing early-weighted trajectory supervision, and evaluating destination correctness through hierarchical matching and curriculum learning. Experimental results show that RLVR-trained LLMs substantially improve over zero-shot LLMs and representative deep learning baselines, especially on destination-related metrics. Among the evaluated RLVR-trained variants, 4B LLMs achieve the best overall performance, suggesting that reward-compatible optimization and task-specific capacity matching are more important than simply using larger 8B or 14B LLMs. The results also show that LSTM remains a strong deep learning baseline under limited fine-tuning data, while Transformer-style spatio-temporal models typically require larger datasets and richer structured inputs. Overall, this work advances semantic, verifier-aligned maritime forecasting for operational decision support.

Hongwei Wang, Miao Zhou, Fengde Wang +10

Institute of High Performance Computing (IHPC), A*STAR, Singapore 138632, Singapore. · The Key Laboratory of Road and Traffic Engineering, Ministry of Education, Tongji University, Shanghai 201804, China. · Meituan Inc., Shenzhen, China. +3

RL for Language Models Vessel Trajectory Prediction Reinforcement Learning with Verifiable Rewards Trajectory Prediction

Jun 7, 2026cs.AI

PAEC: Position-Aware Entropy Calibration for LLM Reasoning in RLVR

Reinforcement learning with verifiable rewards (RLVR) improves large language model reasoning but often suffers from rapid policy-entropy collapse, where the policy prematurely concentrates on narrow high-probability reasoning paths. While global entropy regularization can encourage exploration, uniformly increasing entropy across all token positions is inefficient for long reasoning trajectories, where many tokens are not decision-relevant. We propose Position-Aware Entropy Calibration (PAEC), a token-level entropy-management framework that constructs a soft mask from local top-p entropy and top-two candidate competition, and applies an anchor-based lower-bound penalty to prevent selected-position entropy collapse. Experiments on five mathematical reasoning benchmarks show that PAEC improves macro-average majority-vote performance over strong RLVR baselines, with clear gains on AIME-style tasks. Our results suggest that entropy management in reasoning RL should be formulated as selective exploration allocation over decision-sensitive positions rather than uniform randomness injection.

Shumeng Yang, Yisu Liu, Jiayi Zheng +2

Institute of Automation, Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences · School of Artificial Intelligence, Beijing University of Posts and Telecommunications +2

RL for Language Model Reasoning Maximum Entropy RL Reinforcement Learning with Verifiable Rewards LLM Reasoning

Jun 7, 2026cs.LG

Sparrow: Sparse Rollout for Stable and Efficient Long-context RL of Large Language Models

Despite being powerful, reinforcement learning with verifiable rewards (RLVR) induces extremely long COT, making it computationally expensive. Since RLVR per-step cost is dominated by long-context rollout generation, sparse attention offers a promising way to accelerate dense rollout. However, sparse rollouts require a delicate stability-efficiency tradeoff: overly aggressive sparsity causes collapse, while overly lenient sparsity gives insufficient speedup. In this work, we study this tradeoff through sparse-to-dense actor-policy mismatch. We first observe that sparse rollout collapse is not driven by uniform degradation across tokens: most sparse tokens align perfectly with dense even under aggressive sparsity. Motivated by this, we hypothesize that sparse rollout training remains stable if the lower tail of per-token actor-policy mismatch stays above a critical threshold throughout the trajectory. We introduce a dynamic sparsity schedule that keeps this tail statistic constant during generation and validate our hypothesis. Across Qwen3 thinking-family models, keeping the tail mismatch statistic near a consistent threshold generally enables stable training. We then use a cost model to find the sparsity schedule for maximum speedup under this mismatch threshold, achieving 2.2x, 2.4x, and 2.0x rollout speedups when training Qwen3-1.7B, Qwen3-4B, and Qwen3-8B. Empirically, we show the thresholds generalize to a larger model (Qwen3-14B) and another RL domain (coding). Finally, our analysis naturally motivates DistillSparse: lightweight LoRA-based distillation on sparse rollout lets more aggressive sparsity reach the same sparse-to-dense mismatch threshold, yielding higher speedup.

Yang Zhou, Ranajoy Sadhukhan, Zhaofeng Sun +7

Carnegie Mellon University · Cornell University · Intel +1

RL for Language Model Reasoning Sparse Attention Reinforcement Learning with Verifiable Rewards

Jun 6, 2026cs.CL

CATPO: Critique-Augmented Tree Policy Optimization

Reinforcement learning with verifiable rewards (RLVR) has become a dominant paradigm for improving the reasoning capabilities of large language models (LLMs). Recent tree-based methods such as TreeRPO extend flat trajectory sampling with tree-structured rollouts to obtain dense, step-level reward signals without a separate process reward model. However, not all trees are equally informative: trees where all leaves succeed, all leaves fail, or the policy already predicts the reward distribution contribute little to gradient updates, wasting compute. We introduce CATPO (Critique-Augmented Tree Policy Optimization), which diagnoses and addresses this waste at the tree level. CATPO first scores each tree via a tree informativeness score, F(T), combining leaf-outcome diversity with policy-reward decorrelation at zero extra compute. For dead-wrong trees where all branches fail, CATPO applies critique-guided healing: it locates the shallowest failure point, generates a natural-language critique, and grafts refined continuations to recover training signal. Finally, an informativeness-weighted loss scales each tree's gradient contribution by its normalized score, concentrating parameter updates on the most informative trees while preserving overall gradient magnitude. Experiments on Qwen2.5-Math-1.5B trained with the MATH dataset show that CATPO achieves 37.5% macro accuracy across four benchmarks (AIME24, MATH-500, OlympiadBench, and MinervaMath), improving over TreeRPO by 1.9% and GRPO by 4.8%.

Ayush Singh, Umang Goyal, Ankur Dahiya

Vision and Language Group Indian Institute of Technology Roorkee Roorkee, Uttarakhand, India

RL for Language Models Reinforcement Learning RL for Language Model Reasoning Mathematical Reasoning Reinforcement Learning with Verifiable Rewards

Jun 6, 2026cs.LG

ConSteer-RL: Steering Reasoning Capabilities in Large Language Models via Confidence-Aware Reinforcement Learning

Reinforcement Learning from Verifiable Rewards (RLVR) has recently become a key paradigm for improving the reasoning abilities of Large Language Models (LLMs), yet it remains limited by sparse binary rewards and its ignorance of model-internal uncertainty. In this paper, we propose ConSteer-RL, a simple yet effective framework that integrates token-level confidence signals derived from model log-probabilities into RLVR training. Specifically, building upon the Group Relative Policy Optimization (GRPO) framework, we construct a confidence-aware reward by aggregating per-token probabilities into a scalar confidence score and incorporating it into an awareness-based reward shaping mechanism that penalizes overconfident errors while reinforcing correct and confident reasoning. Experimental results demonstrate that ConSteer-RL consistently outperforms strong GRPO baselines, achieving average improvements of 2.3%-4.0% across different model scales.

Qing Miao, Yiming Zhao, Jing Yang +5

Xi’an Jiaotong University · University of Science and Technology of China

Reward Shaping RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards

Jun 6, 2026cs.CV

DyCo-RL: Dynamic Cross-Modal Coordination for Visual Reasoning

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a leading paradigm for enhancing visual reasoning in Multimodal Large Language Models (MLLMs). However, existing RLVR methods optimize primarily for the reasoning outcome and overlook how that outcome is produced: as a chain-of-thought unfolds, some tokens must extract evidence from the image while others must anchor to the preceding textual context, yet a single sequence-level reward provides no signal about whether each token draws on the modality its role demands. Token-level analyses and controlled interventions reveal that tokens frequently under-attend to their designated modality, and that this coordination breakdown may contribute to reasoning failures. Motivated by these findings, we propose DyCo-RL, which integrates dynamic cross-modal coordination into RLVR optimization. Specifically, DyCo-RL uses the Fisher-Rao geodesic distance to measure within-modality attention shifts, assigning tokens to either visually-oriented or text-oriented functional roles. It then evaluates the alignment between a token's actual attention allocation and its assigned role, leveraging this score for alignment-guided advantage reweighting during policy optimization. Extensive experiments using 11K examples for RL training demonstrate that the algorithm-agnostic DyCo-RL, when applied to Qwen2.5-VL-3B/7B and Qwen3.5-27B, improves the average performance of all four evaluated RLVR algorithms across seven benchmarks spanning visual-centric and mathematical reasoning.

Hangui Lin, Yan Shu, Zhengyang Liang +8

BAAI · University of Trento · Singapore Management University +1

Cross-Modal Alignment VLM Reasoning Cross-Modal Attention Reinforcement Learning with Verifiable Rewards RL for VLMs

Jun 6, 2026cs.LG

The Easy, the Hard, and the Learnable: Confidence and Difficulty-Adaptive Policy Optimization for LLM Reasoning

RL with verifiable rewards can substantially improve LLM reasoning, yet standard GRPO-style training often treats easy, hard, and learnable questions alike through uniform sampling and weighting, leading to inefficient compute allocation. We study GRPO by tracking token log-probabilities, group-normalized advantages, and the induced token-level update weights. This reveals three recurring dynamics as training proceeds: (1) confidence inflation, (2) advantage contraction, and (3) hierarchical convergence. These findings suggest that the utility of each update depends strongly on both question difficulty and the model's current competence. Motivated by this, we propose Confidence and Difficulty-adaptive Policy Optimization (CoDaPO), which assigns each question a bounded value from rollout confidence and empirical difficulty. CoDaPO then uses this value to reweight policy updates and resample high-value learnable questions within mini-batches, thereby increasing discovery within the learnable band under a fixed compute budget. Across twelve benchmarks, CoDaPO consistently improves accuracy over existing RL methods. Our code is publicly available at https://github.com/tmlr-group/CoDaPO.

Zhanke Zhou, Xiangyu Lu, Chentao Cao +4

1TMLR Group, Department of Computer Science, Hong Kong Baptist University · 2Stanford University · 3Sydney AI Centre, The University of Sydney

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

Jun 5, 2026cs.AI

Teaching the Way, Not the Answer: Privileged Tutoring Distillation for Multimodal Policy Optimization

Recent post-training methods, particularly Reinforcement Learning with Verifiable Rewards (RLVR), have significantly enhanced the reasoning ability of Large Vision-Language Models (LVLMs). However, the sparse nature of verifiable rewards provides little token-level supervision for failed rollouts, often leading to inefficient exploration in complex multimodal reasoning tasks. Although policy distillation can offer dense guidance, external teacher based methods introduce substantial computational overhead, while answer conditioned tuning methods may expose answer-level information and induce shortcut-like generation behavior. To address these limitations, we propose PTD-PO, a Privileged Tutoring Distillation Policy Optimization framework for RLVR that provides dense guidance without exposing the answer to the student policy. Specifically, PTD-PO constructs structured privileged hints from spatial attention guidance and intermediate textual reasoning steps, and uses them through in-context learning to produce step-wise token-distribution supervision. The student is still optimized under the original answer-free context, and its failed rollouts are aligned with the hint-augmented reference model at the token-distribution level. To further stabilize distillation under the distribution shift between guided and unguided contexts, we introduce a Top-K Jensen-Shannon divergence objective that focuses alignment on informative token probabilities while reducing memory overhead. Experiments on LVLMs ranging from 2B to 8B parameters show that PTD-PO consistently outperforms RLVR and distillation baselines, mitigates entropy collapse, and improves complex multimodal reasoning performance.

Shizhe Xiang, Ke An, Wenlong Yu +4

1Tianjin University · 2Beijing Institute of Technology · 3Singapore Management University +2

Large Vision-Language Models Multimodal Reasoning Reinforcement Learning with Verifiable Rewards On-Policy Distillation RL for VLMs

Jun 4, 2026cs.SE

TLA-Prover: Verifiable TLA+ Specification Synthesis via Preference-Optimized Low-Rank Adaptation

TLA+ is a formal specification language for verifying distributed systems and safety-critical protocols. Large language models (LLMs) frequently produce TLA+ specifications that fail the TLC model checker for semantic reasons. Across 25 LLMs, the best public baseline is 26.6% syntactic parse and 8.6% semantic model-check. We present TLA-Prover, a 20-billion-parameter model for TLA+ specification synthesis. Training combines supervised fine-tuning (SFT) on verified examples with repair-based group-relative policy optimization (GRPO). In the GRPO stage, the model learns to fix its own rejected specifications. We also train a direct preference optimization (DPO) variant from the same SFT checkpoint as an ablation. TLC provides the reward signal directly, with no learned reward model. Four tiers grade each output: Bronze (parses), Silver (no warnings), Gold (passes TLC), and Diamond. To reach Diamond, the model's correctness property is automatically altered in a small way; TLC must then detect a violation. If TLC still passes, the property was always-true and contributes nothing; the output fails Diamond. TLA-Prover reaches 9/30 (i.e. pass@1 = 30%) at both Gold and Diamond on a held-out 30-problem benchmark. This is roughly 3.5x the 8.6% untuned baseline. The DPO variant reaches 20% at Diamond. Gold and Diamond coincide at every checkpoint; this prevents the trivial-property failure mode.

Eric Spencer, Arslan Bisharat, Brian Ortiz +6

Department of Computer Science, Loyola University Chicago, Chicago, IL 60660, USA

LLM-Based Program Synthesis Formal Verification Reinforcement Learning with Verifiable Rewards

Jun 4, 2026cs.LG

MDP-GRPO: Stabilized Group Relative Policy Optimization for Multi-Constraint Instruction Following

Reinforcement learning with verifiable rewards is ideal for multi-constraint instruction following, yet standard group-relative policy optimization (GRPO) becomes unstable under discrete, low-dispersion rewards, where within-group reward distributions are frequently homogeneous. We identify and formalize three pathologies of z-score group normalization in this regime: low-variance amplification, mean-centering blindness, and zero-variance collapse. To address them, we propose MDP-GRPO, which stabilizes learning through (1) multi-temperature sampling to increase reward dispersion, (2) dual-anchor advantages to restore gradients in homogeneous groups and stop mean-centering blindness, (3) prospect-theoretic shaping to bound updates and penalize violations based on Kahneman and Tversky's theory, and (4) asymmetric KL regularization. Evaluated on FollowBench, IFEval, and a curated multi-constraint dataset, MDP-GRPO outperforms standard GRPO, improving strict constraint satisfaction by up to 5.0% on Llama-3.2-3B. Our method also enables stable convergence with small group sizes while preserving general capabilities on MMLU and ARC.

Mohammad Mahdi Salmani-Zarchi, Zahra Rahimi, Heshaam Faili +1

Department of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, Iran · Department of Statistics, Mathematics and Computer Science, Allameh Tabataba’i University, Tehran, Iran

Group Relative Policy Optimization Instruction Following Reinforcement Learning with Verifiable Rewards Policy Learning

Jun 4, 2026cs.AI

A Pre-Registered Causal Partition of Self-Consistency Elicitation and Reward Design in RLVR

Reinforcement learning from verifiable rewards (RLVR) improves reasoning even when the reward signal is spurious -- assigning credit to the group-plurality answer rather than a ground-truth verifier. Practitioners commonly interpret naive = acc(TRUE) - acc(RANDOM) as the reward-design effect. We prove this estimand is systematically biased: it conflates self-consistency elicitation (sharpening the policy toward its modal answer via majority pseudo-reward) with genuine reward-design signal. Using a controlled tabular-GRPO simulator we derive an exact telescoping decomposition total = null + elicit + rd and measure each term across five prior-strength levels. The reward-design fraction of the naive estimator ranges from 0.139 at weak prior (ps=0.20) to 0.05 at strong prior (ps=0.80), with the elicitation term flipping sign at the self-consistency crossover. A pre-registered 2x2x2 factorial confirms non-additivity (interaction ratio 0.385; AxC effect -0.089). A points-vs-bounds pilot gate shows strong-prior regimes are point-identified while near-crossover regimes are only bounded. Re-audits of two named published results yield ELICITATION DOMINATED (elicitation share 0.98) and REWARD DESIGN DOMINATED (rd share 1.18) verdicts respectively, demonstrating the diagnostic value of the partition. We pre-commit to submit regardless of flip outcome; a non-flip is a finding of equal standing. We release a reusable one-command harness for any alignment paper to run the same audit.

Yuze Gao

Reinforcement Learning Self-Consistency Decoding Reinforcement Learning with Verifiable Rewards Causal Inference Reward Design for RL

Jun 4, 2026cs.LG

SALT: When More Rollouts Don't Help in Group-Based Policy Optimization and How to Make Them Matter

Reinforcement learning with verifiable rewards (RLVR) often adopts GRPO-style group-relative updates, sampling multiple rollouts per prompt to construct normalized learning signals. However, merely increasing the number of rollouts does not reliably strengthen learning: under GRPO-style group normalization, per-rollout policy-gradient features can concentrate into a low-rank, signed geometry, causing substantial cancellation during aggregation and weakening the effective update. We address this failure mode with SALT, a Subspace-Adaptive geometry pLug-in componenT that uses sample-wise gradient geometry to reweight the coefficients of group-relative updates. SALT estimates a dominant shared subspace from the mini-batch Gram geometry, decomposes group-relative coefficients into shared and residual channels, and adaptively amplifies the residual channel when signed cancellation is severe. Across diverse reasoning-oriented RLVR benchmarks and model scales, SALT improves effective update geometry and performance without modifying the reward model or the rollout sampling procedure

Powei Chang, Jinpeng Zhang, Chaoqun Sun +6

Bilibili Inc. · Fudan University · Zhejiang University

Policy Gradient Group Relative Policy Optimization Reinforcement Learning with Verifiable Rewards Policy Learning

Jun 3, 2026cs.LG

Reinforcement Learning from Rich Feedback with Distributional DAgger

Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger, where the learner has local access to an expert distribution on states visited by the current policy. This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient {conduct rich credit assignment by propagating} future expert-student disagreement back to earlier decisions. We show that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement: even when the expert has higher reward, their updates may increase probability on worse actions. In contrast, we show that forward cross-entropy admits monotonic policy improvement and enjoys guarantees on regret. We further show that our objective optimizes a lower bound on teacher-weighted likelihood of success, leading to improved Pass@N. Empirically, our approach, DistIL, improves over RLVR and RL with self-distillation baselines across a variety of domains: scientific reasoning, coding, and solving hard mathematical problems.

Rishabh Agrawal, Jacob Fein-Ashley, Paria Rashidinejad

University of Southern California

Distributional RL RL for Language Model Reasoning Credit Assignment in RL Imitation Learning Reinforcement Learning with Verifiable Rewards Policy Learning

Jun 3, 2026cs.LG

Policy-Conditioned Counterfactual Credit for Verifiable Reinforcement Learning of Long-Horizon Language Agents

Reinforcement learning with verifiable rewards improves reasoning and tool use, yet long-horizon language agents still learn unsupported evidence chains, belief drift, and shortcut actions that satisfy terminal checks. Existing process rewards are mostly correlational: they reward retrieval-, reflection-, or verification-like steps without estimating whether the step contributes to final verified success under a specified intervention. We propose CVT-RL, a constrained policy-gradient algorithm with dense verifiable rewards, intervention-validity gating, and a policy-conditioned counterfactual contribution (PCCC) estimator. Deletion, semantic substitution, evidence substitution, and tool-output perturbation define separate controlled interventions; continuations are sampled from a frozen reference policy, and a selection-adjusted doubly robust estimator augments the advantage. Belief control uses only prefix-observable labels, while an augmented Lagrangian constrains unsupported claims, skipped verification, tool tampering, and unsafe calls. On long-context QA, ALFWorld, ScienceWorld, and web/tool tasks, CVT-RL improves average task success from 71.8% for compute-matched non-causal RL and 75.4% for an information-matched counterfactual-process baseline to 78.9%, improves evidence F1 from 78.9 to 82.8 over the information-matched baseline, and reduces measured hacking from 7.2% to 3.9%. Independent human audit estimates 4.6% hacking for CVT-RL versus 8.1% for the information-matched baseline, and adaptive detector-evasion attacks raise hacking only to 7.1%. Stratified bootstrap and mixed-effects tests give p<0.01 after Holm correction for all primary metrics. Carefully scoped counterfactual credit, paired with validity gating, diagnostics, and verifiable constraints, provides a reproducible route toward more reliable long-horizon RL for language agents.

Renwei Meng

Ahu

Credit Assignment in RL Long-Horizon Agent Evaluation Constrained RL Reinforcement Learning with Verifiable Rewards Counterfactual Learning RL for LLM Agents

Jun 3, 2026cs.CL

GRAIL: Gradient-Reweighted Advantages for Reinforcement Learning with Verifiable Rewards

Reinforcement learning with verifiable rewards (e.g. GRPO) is now a common way to improve mathematical reasoning in Large Language Models (LLMs). However, current methods usually broadcast one sequence-level advantage to all tokens, or use costly process reward models (PRMs) for step-level supervision. Uniform advantage distribution assumes that all tokens contribute equally to the final reward. This dilutes the gradient signal, since flawed reasoning steps and filler words are updated as strongly as valid logical inferences. To address this, we introduce Gradient-Reweighted Advantage (GRAIL), an intrinsic token-wise advantage reweighting method. GRAIL uses gradient-activation saliency to place more weight on tokens that are more locally sensitive to the final answer. Evaluations across five models from the Qwen3, R1-distilled and OctoThinker families show that GRAIL consistently outperforms GRPO. GRAIL achieved an average improvement of 3.60% in accuracy and 3.05% in Pass@3, demonstrating that fine-grained reasoning alignment can be achieved without process-level supervision.

Tej Deep Pala, Vernon Toh, Soujanya Poria

DeCLaRe Lab, Nanyang Technological University

RL for Language Model Reasoning Credit Assignment in RL Reinforcement Learning with Verifiable Rewards LLM Reasoning

Jun 3, 2026cs.AI

SCI-PRM: A Tool Aware Process Reward Model for Scientific Reasoning Verification

While Process Reward Models (PRMs) have achieved remarkable success in mathematical reasoning, their application in complex scientific domains-such as biology, chemistry, and physics remains largely unexplored. Scientific problems demand not only logical rigor but also factual consistency and the precise usage of domain-specific tools, areas where current models often suffer from hallucinations and lack of verification. In this paper, we first construct SCIPRM70K, a large-scale dataset featuring Chain-of-Tool trajectories that explicitly interleave reasoning with the execution of scientific tools. Building upon this, we train an efficient reward model called Sci-PRM to provide fine-grained supervision on tool selection, execution accuracy, and result interpretation at each step in one inference. Experiments demonstrate that Sci-PRM significantly enhances foundation models in two key aspects: (1) it enables effective test-time scaling via Best-of-N selection; and (2) when integrated into Reinforcement Learning, it serves as a dense reward signal that mitigates the critical issue of advantage disappearance, allowing the model to break through existing performance ceilings.

Xiangyu Zhao, Henry Hengyuan Zhao, Yiheng Wang +7

The Hong Kong Polytechnic University · National University of Singapore · Shanghai AI Lab +3

Process Reward Models Scientific Reasoning Reinforcement Learning with Verifiable Rewards RL for Tool Use

Jun 3, 2026cs.LG

Rollout-Level Advantage-Prioritized Experience Replay for GRPO

Reinforcement learning from verifiable rewards with GRPO is a standard approach for post-training reasoning LLMs. It remains sample inefficient. Each rollout is used for a single gradient update and then discarded. Naive replay is not well suited in this setting because LLM policies drift quickly per gradient step. Stored rollouts therefore become stale and can destabilize training. We propose a rollout-level replay buffer for GRPO that stores and samples individual rollouts rather than whole groups. The buffer bounds staleness through age eviction. Any rollout older than tau_max training steps is removed. The buffer also preserves on-policy data via fresh-anchored composition. Each batch keeps its fresh on-policy rollouts and then concatenates replay rollouts drawn separately from the buffer. We prioritize replay by per-rollout advantage magnitude and recycle individual rollouts whose advantages are large. Across three Qwen3-Base scales on five math benchmarks, our method outperforms GRPO and naive replay baselines. Gains are positive at every scale and reach +1.66 pp on the five-benchmark average at 4B. Under an AES metric that jointly measures accuracy and token efficiency, our method is the only condition with a positive margin over GRPO at every scale.

Gyeongtae Yoo, Sanghyeok Park, Soohyuk Jang +2

Department of Electrical and Computer Engineering, Seoul National University · Interdisciplinary Program in AI, Seoul National University · AIIS, ASRI, INMC, and ISRC, Seoul National University

RL for Language Model Reasoning Group Relative Policy Optimization Experience Replay Reinforcement Learning with Verifiable Rewards RL Post-Training Policy Learning+1

Jun 3, 2026cs.LG

GeoMin: Data-Efficient Semi-Supervised RLVR via Geometric Distribution Modeling

Reinforcement learning with verifiable rewards (RLVR) significantly advances LLM reasoning, yet it faces a dilemma: standard supervised scaling is throttled by high annotation costs, while unsupervised alternatives suffer from severe model collapse. Recent semi-supervised RLVR methods address this by using a small labeled set to guide unlabeled data, achieving a promising trade-off between training efficacy and annotation cost. However, they suffer from a severe data-efficiency bottleneck due to the reliance on coarse performance heuristics, leaving a vast majority of valuable instances underutilized. To this end, we propose GeoMin, which models global feature distributions on labeled data to decode the structural discrepancy between correct and incorrect rollouts, thereby establishing a robust prior to assess the reliability of self-reward signals and fully unleash the potential of unlabeled data. Empirically, GeoMin outperforms the strongest baselines by +4.1% and even surpasses fully supervised models with only 10% of the annotations, demonstrating remarkable data efficiency.

Guangcheng Zhu, Shenzhi Yang, Haobo Wang +9

1Zhejiang University · 2Ant Group

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Semi-Supervised Learning Data-Efficient Learning