Title: Kalman Filter Enhanced Group Relative Policy Optimization for Language Model Reasoning
Primary area: foundation or frontier models, including LLMs
Keywords: Language Model, Reasoning, Reinforcement Learning, Kalman Filter

Abstract: The advantage function is a central concept in RL that helps reduce variance in policy gradient estimates. Recently, for language modeling, Group Relative Policy Optimization (GRPO) was 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 high variance when the reward advantage is inaccurately predicted. In this work, we propose Kalman Filter Enhanced Group Relative Policy Optimization (KRPO) model, by using lightweight Kalman filtering to dynamically estimate the latent reward baseline and uncertainty. This filtering technique replaces the naive group mean, 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 language models. Through the accuracies 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://anonymous.4open.science/r/KRPO-E1D3.

TL;DR: KRPO extends GRPO by using a Kalman filter to replace the group mean reward, improving reward baseline and uncertainty estimation for better advantage estimates and policy performance, without adding learned parameters.