提出更高效稳定的强化学习优化算法，无需价值函数评估

Group Relative Policy Optimization (GRPO), recently introduced by DeepSeek, is a critic-free reinforcement learning algorithm for fine-tuning large language models. GRPO replaces the value function in Proximal Policy Optimization (PPO) with group-normalized rewards while retaining PPO-style token-level importance sampling based on an old policy. Our theoretical analysis reveals that the GRPO update rule estimates the policy gradient at the old policy rather than the current one; however, since the old policy is refreshed every few steps, the resulting discrepancy remains small and the induced bias is negligible in practice. To empirically validate this insight, we conduct an ablation study that entirely removes importance sampling and performs multiple optimization steps using gradients estimated at a fixed old policy. Remarkably, this simplified variant attains performance comparable to standard GRPO. Motivated by this finding, we propose Trajectory-level Importance-Corrected GRPO (TIC-GRPO), a new algorithm that replaces token-level importance ratios with a single trajectory-level probability ratio, thereby yielding an estimate of the current policy gradient while preserving the critic-free structure. Furthermore, we present the first convergence analysis for GRPO-style methods and show that TIC-GRPO converges faster than GRPO. Finally, empirical results across math reasoning and coding tasks demonstrate the superiority of TIC-GRPO.