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arXiv 2605.07331cs.LGcs.AI
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重新思考LLM策略优化中的重要性采样:从累积token视角

Rethinking Importance Sampling in LLM Policy Optimization: A Cumulative Token Perspective

UIUC(伊利诺伊大学香槟分校);University of Michigan(密歇根大学);Amazon(亚马逊)

Yuheng Zhang, Chenlu Ye, Shuowei Jin, Changlong Yu, Wei Xiong, Saurabh Sahu, Nan Jiang

AI总结:

本文提出CTPO,通过累积token重要性采样比解决偏倚-方差困境,结合位置自适应裁剪提升稳定性,实现更一致的正则化,在数学推理基准上表现最佳。

摘要:

强化学习,包括可验证奖励的强化学习(RLVR),已发展为LLM后训练的强大方法。这些方法的核心是设计用于离策略策略梯度估计的重要采样(IS)比。现有方法面临偏倚-方差困境:token级IS比如PPO和GRPO所采用,通过忽略前缀状态分布不匹配引入偏倚;全序列比提供精确轨迹级修正但因每token比的乘法累积导致高方差,而GSPO通过长度归一化提升数值稳定性但偏离精确全序列IS修正。本文识别出累积token IS比,即到位置t的每token比的乘积,作为解决该困境的理论原则性方案。证明在token级策略梯度公式下,该比值为每个token级梯度项提供无偏前缀修正,并具有严格低于全序列比的方差。基于此洞察,我们提出CTPO(累积token策略优化),将累积token IS比与位置自适应裁剪结合,后者根据自然的累积对数比的√t增长缩放对数空间裁剪界。这导致更一致的token位置正则化。我们在工具集成推理设置上实现并评估CTPO, 在多个具有挑战性的数学推理基准上,相比强大的GRPO和GSPO基线,实现了最佳的平均性能。代码将在https://github.com/horizon-llm/CTPO上提供。

英文摘要:

Reinforcement learning, including reinforcement learning with verifiable rewards (RLVR), has emerged as a powerful approach for LLM post-training. Central to these approaches is the design of the importance sampling (IS) ratio used in off-policy policy-gradient estimation. Existing methods face a fundamental bias-variance dilemma: token-level IS ratios, as adopted by PPO (Schulman et al., 2017) and GRPO (Shao et al., 2024), introduce bias by ignoring prefix state distribution mismatch; full sequence ratios provide exact trajectory-level correction but suffer from high variance due to the multiplicative accumulation of per-token ratios, while GSPO (Zheng et al., 2025) improves numerical stability via length normalization at the cost of deviating from the exact full-sequence IS correction. In this work, we identify the cumulative token IS ratio, the product of per-token ratios up to position $t$, as a theoretically principled solution to this dilemma. We prove that, under the token-level policy-gradient formulation, this ratio provides an unbiased prefix correction for each token-level gradient term and has strictly lower variance than the full sequence ratio. Building on this insight, we propose CTPO (Cumulative Token Policy Optimization), which combines the cumulative token IS ratio with position-adaptive clipping that scales log-space clip bounds according to the natural $\sqrt{t}$ growth of the cumulative log-ratio. This yields more consistent regularization across token positions. We implement and evaluate CTPO in the tool-integrated reasoning setting on several challenging mathematical reasoning benchmarks, achieving the best average performance across both model scales compared with strong GRPO and GSPO baselines. Code will be available at https://github.com/horizon-llm/CTPO.

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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