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arXiv 2602.05946cs.LGstat.ML

f-GRPO 与 beyond:基于发散性的强化学习算法用于通用大语言模型对齐

f-GRPO and Beyond: Divergence-Based Reinforcement Learning Algorithms for General LLM Alignment

Department of Statistics, Purdue University(普渡大学统计学系);Department of Statistics, Michigan State University(密歇根州立大学统计学系)

Rajdeep Haldar, Lantao Mei, Guang Lin, Yue Xing, Qifan Song

AI总结:

本文提出f-GRPO和f-HAL算法,通过发散性估计提升大语言模型对齐效果,在数学推理任务中改进GRPO并缓解奖励黑客问题。

摘要:

近期研究表明,偏好对齐目标可解释为对齐分布与未对齐分布之间的发散估计器,从而为设计对齐损失提供了原理性方法。然而,这一观点目前仅限于基于偏好的监督。我们将其扩展到通用大语言模型对齐,包括可验证奖励的强化学习(RLVR),其中对齐反馈仅作为标量奖励提供。我们引入f-组相对策略优化(f-GRPO),一种在线强化学习目标,以及f-混合对齐损失(f-HAL),结合在线奖励优化与离线偏好监督。我们证明这些目标估计由高于或低于平均奖励响应诱导的奖励对齐分布与奖励未对齐分布之间的f-发散性,并证明对齐后预期奖励的提升。实证上,f-GRPO在数学推理RLVR任务中优于GRPO,而混合f-HAL在可验证奖励不可用且必须使用学习奖励模型时缓解在线安全对齐中的奖励黑客问题。

英文摘要:

Recent work shows that preference alignment objectives can be interpreted as divergence estimators between aligned (preferred) & unaligned (less-preferred) distributions, yielding a principled recipe for designing alignment losses. However, this view has so far been limited to preference-based supervision. We extend it to general LLM alignment, including reinforcement learning with verifiable rewards (RLVR), where alignment feedback is given only as scalar rewards. We introduce $f$-Group Relative Policy Optimization ($f$-GRPO), a class of on-policy RL objectives, and $f$-Hybrid Alignment Loss ($f$-HAL), which combines on-policy reward optimization with off-policy preference supervision. We show that these objectives estimate $f$-divergences between reward-aligned & reward-unaligned distributions induced by above- & below-average reward responses, and prove expected reward improvement after alignment. Empirically, $f$-GRPO improves over GRPO on math-reasoning RLVR tasks, while hybrid $f$-HAL mitigates reward hacking in on-policy safety alignment when verifiable rewards are unavailable and learned reward models must be used.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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