Bellman-Consistent Trajectory RL for LLM Arithmetic Reasoning
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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.
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.
arXiv:2608. 16739v1 Announce Type: new Abstract: Reinforcement learning algorithms for Large Language Models (LLMs) are largely distinguished by their variance reduction strategy.
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.
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.
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...