Improving the reasoning abilities of Large Language Models (LLMs) has been a continuous topic recently. But most relevant works are based on outcome rewards at the trajectory level, missing fine-grained supervision during the reasoning process. Other existing training frameworks that try to combine process signals together to optimize LLMs also rely heavily on tedious additional steps like MCTS, training a separate reward model, etc., doing harm to the training efficiency. Moreover, the intuition behind the process signals design lacks rigorous theoretical support, leaving the understanding of the optimization mechanism opaque. In this paper, we propose Process Reward Learning (PRL), which decomposes the entropy regularized reinforcement learning objective into intermediate steps, with rigorous process rewards that could be assigned to models accordingly. Starting from theoretical motivation, we derive the formulation of PRL that is essentially equivalent to the objective of reward maximization plus a KL-divergence penalty term between the policy model and a reference model. However, PRL could turn the outcome reward into process supervision signals, which helps better guide the exploration during RL optimization. From our experiment results, we demonstrate that PRL not only improves the average performance for LLMs' reasoning ability measured by average @ n, but also broadens the reasoning boundary by improving the pass @ n metric. Extensive experiments show the effectiveness of PRL could be verified and generalized.

翻译：提升大语言模型（LLMs）的推理能力是近期持续关注的话题。然而，现有研究大多基于轨迹层面的结果奖励，缺乏对推理过程的细粒度监督。其他尝试结合过程信号以优化LLMs的训练框架，也严重依赖如蒙特卡洛树搜索（MCTS）、训练独立奖励模型等繁琐的额外步骤，损害了训练效率。此外，过程信号设计背后的直觉缺乏严格的理论支持，导致对优化机制的理解仍不清晰。本文提出过程奖励学习（PRL），将熵正则化强化学习目标分解为中间步骤，并据此为模型分配严格定义的过程奖励。我们从理论动机出发，推导出PRL的公式化表达，其本质上等价于奖励最大化目标加上策略模型与参考模型之间的KL散度惩罚项。然而，PRL能够将结果奖励转化为过程监督信号，从而在强化学习优化过程中更好地指导探索。实验结果表明，PRL不仅通过平均@n指标提升了LLMs推理能力的平均性能，还通过改进pass@n指标拓展了推理边界。大量实验验证了PRL的有效性与泛化能力。