Kalman Filter Enhanced GRPO for Reinforcement Learning-Based Language Model Reasoning

Abstract: Reward baseline is important for Reinforcement Learning (RL) algorithms to reduce variance in policy gradient estimates. Recently, for language modeling, Group Relative Policy Optimization (GRPO) is proposed to compute the advantage for each output by subtracting the mean reward, as the baseline, for all outputs in the group. However, it can lead to inaccurate advantage estimates in environments with highly noisy rewards, potentially introducing bias. In this work, we propose a model, called Kalman Filter Enhanced Group Relative Policy Optimization (KRPO), by using lightweight Kalman filtering to dynamically estimate the latent reward mean and variance. This filtering technique replaces the naive batch mean baseline, enabling more adaptive advantage normalization. Our method does not require additional learned parameters over GRPO. This approach offers a simple yet effective way to incorporate multiple outputs of GRPO into advantage estimation, improving policy optimization in settings where highly dynamic reward signals are difficult to model for LLMs. Through accuracy and rewards obtained from math question answering and reasoning, we show that using a more adaptive advantage estimation model, KRPO can improve the stability and performance of GRPO. The code is available at https://github.com/billhhh/KRPO_LLMs_RL.