The paper introduces a Bellman-consistent trajectory reinforcement learning approach for large language model (LLM) arithmetic reasoning, called Trajectory Bellman Residual Minimization (TBRM). By converting sparse terminal rewards into dense token-level signals and employing a Reinforce Leave-One-Out (RLOO) strategy to reduce gradient variance, the method improves learning stability. On the Countdown task, TBRM-RLOO achieves Pass@1 scores of 0.55–0.64 and a state-of-the-art Pass@16 accuracy of 76.0–84.0%, surpassing several baseline methods.
By Lianfa Li
arXiv:2601. 11960v3 Announce Type: replace-cross Abstract: Existing reinforcement learning methods for LLM reasoning implicitly assume that the policy generating training trajectories should coincide with the one producing inference responses.
By Jingchu Wang, Bingbing Xu, Yige Yuan, Dan Zhang, Bin Xie, Xiaoqian Sun, Huawei Shen
arXiv:2608. 16739v1 Announce Type: new Abstract: Reinforcement learning algorithms for Large Language Models (LLMs) are largely distinguished by their variance reduction strategy.
By Siddarth Venkatraman, Matthieu Dinot, Laurence Aitchison
arXiv:2606. 29758v1 Announce Type: cross Abstract: Reinforcement Learning from Human Feedback (RLHF) for Large Language Models increasingly relies on critic-free methods as a practical alternative to actor--critic training.
By Doo Hwan Hwang, Kee-Eung Kim
The paper introduces Trajectory-Aware Policy Optimization (TAPO), a new framework for reinforcement learning that addresses the state distribution shift caused by long-horizon autoregressive rollouts in large language models. TAPO derives a state-distribution correction from the off-policy policy gradient, integrates it into the RL objective, and uses a geometric-mean estimator for variance reduction along with length-aware dynamic clipping to stabilize updates. Experiments on eight competition-level benchmarks show TAPO outperforms existing LLM RL methods, achieving up to 48% improvement on mathematical reasoning and 12% on algorithmic coding tasks while enhancing training stability.
By Zhicheng Cai, Weinan Dai, Yuyan Zhou, Wei-Ying Ma, Ya-Qin Zhang, Hao Zhou
arXiv:2608.24696v1 Announce Type: cross
Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) and on-policy distillation (OPD) have become two widely adopted paradigms for post-training lar...
By Wenze Lin, Jiale Zhao, Xitai Jiang, Songde Rao, Yining Li, Shenzhi Wang, Bingxiang He, Gao Huang
The paper introduces the Posterior Concentration Phenomenon (PCP), a length‑dependent failure mode where probability‑based rewards collapse to a narrow interval for long reasoning traces, destabilizing verifier‑free reinforcement learning. To address this, the authors propose RLCPR, a framework that uses uncertainty‑aware data sampling and concentration‑aware regularization to mitigate PCP, improving token efficiency and outperforming state‑of‑the‑art baselines on multiple reasoning benchmarks.
By Shiu-Hong Kao, Yubo Zhao, Zhenyu Tian, Pengzhan Sun, Yicong Li, Angela Yao
arXiv:2607. 04713v1 Announce Type: cross Abstract: Reinforcement learning holds significant potential for training large language models (LLMs) to handle multi-turn interactive tasks.
By Qiang Liu, Taian Guo, Ruizhi Qiao, Xing Sun
arXiv:2603. 25184v2 Announce Type: replace-cross Abstract: Reinforcement learning (RL) has become essential for post-training large language models (LLMs) in reasoning tasks.
By Jiahao Wu, Ning Lu, Shengcai Liu, Kun Wang, Yanting Yang, Bailong Lin, Chen Jason Zhang, Li Qing, Ke Tang
arXiv:2608. 03119v1 Announce Type: new Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) improves LLM reasoning but typically relies on ground-truth (GT) answers, limiting scalability.
By Yongshi Ye, Liang Zhang, Yidong Chen, Xiaodong Shi, Biao Fu
arXiv:2606. 01281v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs).
By Yixiu Mao, Yun Qu, Qi Wang, Heming Zou, Xiangyang Ji
The paper introduces DCRL (Divide-and-Conquer RL), a method that recursively decomposes offline goal-conditioned reinforcement learning trajectories into a balanced binary tree. By training values from the leaves up to the root, DCRL avoids noisy max-based backups and reduces bootstrap depth from linear to logarithmic, thereby limiting error accumulation. Experiments on diverse goal-reaching tasks show that DCRL outperforms prior flat offline GCRL methods, achieving a higher average score on the most challenging long-horizon OGBench tasks.
By Hyeonseong Jeon, Youngwoon Lee