Future-KL Regularized GRPO: Process-Level Credit Assignment from $f$-Divergence Regularization 文章

arXiv:2601.10201v2 Announce Type: replace-cross Abstract: 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 $2\arcsin\sqrt p$. 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.