Recent advances in rule-based reinforcement learning (RL) have significantly
improved the reasoning capability of language models (LMs) with rule-based
rewards. However, existing RL methods — such as GRPO, REINFORCE++, and RLOO —
often suffer from training instability, where large policy updates and improper
clipping can lead to training collapse. To address this issue, we propose
Clipped Policy Gradient Optimization with Policy Drift (CPGD), a novel
algorithm designed to stabilize policy learning in LMs. CPGD introduces a
policy drift constraint based on KL divergence to dynamically regularize policy
updates, and leverages a clip mechanism on the logarithm of the ratio to
prevent excessive policy updates. We provide theoretical justification for CPGD
and demonstrate through empirical analysis that it mitigates the instability
observed in prior approaches. Furthermore, we show that CPGD significantly
improves performance while maintaining training stability. Our implementation
balances theoretical rigor with practical usability, offering a robust
alternative for RL in the post-training of LMs. We release our code at
https://github.com/ModalMinds/MM-EUREKA.