PRL: Process Reward Learning Improves LLMs' Reasoning Ability and Broadens the Reasoning Boundary

Jiarui Yao, Ruida WANG, Hao Bai, Tong Zhang

PRL: Process Reward Learning Improves LLMs' Reasoning Ability and Broadens the Reasoning Boundary: 10 upvotes on Hugging Face Daily Papers, #29 of 38 papers on 2026-01-16. Day-by-day upvote history.

Group Relative Policy Optimization (GRPO) is widely used for critic-free Large Language Model (LLM) post-training, but its KL regularization is usually implemented as a local loss-side token penalty. We show that this misses the policy-gradient signal induced by autoregressive KL regularization. Unlike standard KL-regularized Reinforcement Learning (RL) objectives, GRPO's group normalization induces a non-linear prompt-level utility; for binary verifier rewards, this utility is 2arcsinsqrt p. As a result, reward and KL cannot be fused before normalization without changing the implicit objective. We derive the on-policy gradient of GRPO-style objectives with token-wise f-divergence regularization. The reward term recovers the standardized GRPO advantage, while the regularizer term includes a causal future-regularization return-to-go omitted by local KL losses. For reverse KL, this yields a simple future KL correction: add a reverse cumulative sum of per-token log ratios after advantage construction. The resulting method, Future-KL Regularized Policy Optimization (FRPO), requires no critic or extra model passes. On mathematical reasoning tasks, FRPO improves pass@16 in our main large-model setting while maintaining higher entropy and lower policy drift than conventional loss-side KL baselines.

Paper page on Hugging Face · arXiv

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