arXiv AI
Oct 16

Bellman-Consistent Trajectory RL for LLM Arithmetic Reasoning

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 Machine Learning
Oct 12

Trajectory-Aware Policy Optimization: Closing the State Distribution Gap in Long-Horizon LLM RL

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