# Ratio-Variance Regularized Policy Optimization

arXiv: https://arxiv.org/abs/2605.26784 · HTML: https://mlsanity.com/paper/2605.26784/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 41 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 30 of 35)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Learning Dexterous In-Hand Manipulation](https://mlsanity.com/paper/1808.00177/) (2018)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Safe and Efficient Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1606.02647/) (2016)
- [Implementation Matters in Deep Policy Gradients: A Case Study on PPO and TRPO](https://mlsanity.com/paper/2005.12729/) (2020)
- [VLA-RL: Towards Masterful and General Robotic Manipulation with Scalable Reinforcement Learning](https://mlsanity.com/paper/2505.18719/) (2025)
- [Emergence of Locomotion Behaviours in Rich Environments](https://mlsanity.com/paper/1707.02286/) (2017)
- [Fine-Tuning Large Vision-Language Models as Decision-Making Agents via Reinforcement Learning](https://mlsanity.com/paper/2405.10292/) (2024)
- [Scalable trust-region method for deep reinforcement learning using Kronecker-factored approximation](https://mlsanity.com/paper/1708.05144/) (2017)
- [What Can RL Bring to VLA Generalization? An Empirical Study](https://mlsanity.com/paper/2505.19789/) (2025)
- [V-MPO: On-Policy Maximum a Posteriori Policy Optimization for Discrete and Continuous Control](https://mlsanity.com/paper/1909.12238/) (2019)
- [Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models](https://mlsanity.com/paper/2503.21380/) (2025)
- [Pangu Embedded: An Efficient Dual-system LLM Reasoner with Metacognition](https://mlsanity.com/paper/2505.22375/) (2025)
- [Tapered Off-Policy REINFORCE: Stable and efficient reinforcement learning for LLMs](https://mlsanity.com/paper/2503.14286/) (2025)
- [Klear-Reasoner: Advancing Reasoning Capability via Gradient-Preserving Clipping Policy Optimization](https://mlsanity.com/paper/2508.07629/) (2025)
- [Simple Policy Optimization](https://mlsanity.com/paper/2401.16025/) (2024)
- [Differentiable Trust Region Layers for Deep Reinforcement Learning](https://mlsanity.com/paper/2101.09207/) (2021)
- [Multi-Agent Trust Region Policy Optimization](https://mlsanity.com/paper/2010.07916/) (2020)
- [Wasserstein Policy Optimization](https://mlsanity.com/paper/2505.00663/) (2025)

## Abstract (arXiv)

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 bf R2bf 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. R2VPO 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.