Ratio-Variance Regularized Policy Optimization

Standard on-policy reinforcement learning relies on heuristic clipping to enforce trust regions, but this mechanism imposes a severe cost by indiscriminately truncating high-return yet high-divergence updates. We demonstrate that explicitly constraining the *policy ratio **variance*** provides a principled local approximation to trust-region constraints, eliminating the need for binary hard clipping. By acting as a distributional ''soft brake'', this approach preserves critical gradient signals from novel discoveries while naturally down-weighting and enabling the reuse of stale, off-policy data. We introduce **R$^2$VPO** (Ratio-Variance Regularized Policy Optimization), which implements this constraint via a primal–dual optimization framework. Extensive evaluations across $7$ LLM scales, spanning both fast and slow reasoning paradigms, and $10$ robotic control tasks demonstrate the generality of the proposed approach. R$^2$VPO achieves substantial performance gains on mathematical reasoning benchmarks, with particularly pronounced improvements on smaller models, while significantly improving sample efficiency. Furthermore, it consistently outperforms PPO baselines in continuous control domains, particularly in sparse-reward and dynamic environments. Together, these findings establish ratio-variance regularization as a principled foundation for stable and data-efficient policy optimization.