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

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Abstract:Reinforcement learning, including reinforcement learning with verifiable rewards (RLVR), has emerged as a powerful method for LLM submit-coaching. Central to these approaches is the design of the significance sampling (IS) ratio utilized in off-coverage coverage-gradient estimation. Existing methods face a elementary bias-variance dilemma: token-degree 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 present precise trajectory-level correction but endure from excessive variance due to the multiplicative accumulation of per-token ratios, while GSPO (Zheng et al., 2025) improves numerical stability through size normalization at the cost of deviating from the exact full-sequence IS correction. We show that, under the token-level coverage-gradient formulation, this ratio gives an unbiased prefix correction for each token-degree gradient term and has strictly lower variance than the total sequence ratio. This yields extra constant regularization across token positions. We implement and consider CTPO within the tool-integrated reasoning setting on several difficult mathematical reasoning benchmarks, achieving the most effective common performance across each model scales compared with sturdy GRPO and GSPO baselines. Code can be out there at this https URL.

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