# Rethinking the Divergence Regularization in LLM RL

arXiv: https://arxiv.org/abs/2606.09821 · HTML: https://mlsanity.com/paper/2606.09821/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 36 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 29 of 29)

- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [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)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [Mirror Descent Policy Optimization](https://mlsanity.com/paper/2005.09814/) (2020)
- [Truly Proximal Policy Optimization](https://mlsanity.com/paper/1903.07940/) (2019)
- [Defeating the Training-Inference Mismatch via FP16](https://mlsanity.com/paper/2510.26788/) (2025)
- [Every Step Evolves: Scaling Reinforcement Learning for Trillion-Scale Thinking Model](https://mlsanity.com/paper/2510.18855/) (2025)
- [Prosperity before Collapse: How Far Can Off-Policy RL Reach with Stale Data on LLMs?](https://mlsanity.com/paper/2510.01161/) (2025)
- [Stabilizing Reinforcement Learning with LLMs: Formulation and Practices](https://mlsanity.com/paper/2512.01374/) (2025)
- [Rethinking the Trust Region in LLM Reinforcement Learning](https://mlsanity.com/paper/2602.04879/) (2026)
- [Trust Region-Guided Proximal Policy Optimization](https://mlsanity.com/paper/1901.10314/) (2019)
- [Simple Policy Optimization](https://mlsanity.com/paper/2401.16025/) (2024)
- [TROLL: Trust Regions improve Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2510.03817/) (2025)
- [Ratio-Variance Regularized Policy Optimization for Efficient LLM Fine-tuning](https://mlsanity.com/paper/2601.03320/) (2026)

## Built on by (most cited first, 5 of 5)

- [Stale but Stable: Staleness-Adaptive Trust Regions for Stabilizing Asynchronous Reinforcement Learning](https://mlsanity.com/paper/2607.18722/) (2026)
- [Learning from Your Own Mistakes: Constructing Learnable Micro-Reflective Trajectories for Self-Distillation](https://mlsanity.com/paper/2606.18844/) (2026)
- [Predictive Divergence Masks for LLM RL](https://mlsanity.com/paper/2607.10848/) (2026)
- [Bellman Policy Optimization](https://mlsanity.com/paper/2609.15987/) (2026)
- [CARM: Cancellation-Aware Response Masking for LLM Reinforcement Learning](https://mlsanity.com/paper/2610.02039/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has become a key component of post-training large language models (LLMs). In practice, LLM RL is often off-policy because of training-inference mismatch and policy staleness, making trust-region control essential for stable optimization. Mainstream methods such as PPO and GRPO approximate this control with a ratio-clipping mechanism, but the importance ratio can be a poor proxy for distributional shift in long-tailed vocabularies. Recent work such as DPPO addresses this mismatch by replacing ratio-based clipping with a divergence-based mask, yielding a trust region defined by the sampled token's absolute probability shift. However, DPPO still relies on a hard mask: once a token crosses the trust-region boundary in a harmful direction, its gradient is discarded rather than corrected. To address this, we propose Divergence Regularized Policy Optimization (DRPO), which replaces the hard mask with a smooth advantage-weighted quadratic regularizer on policy shift. DRPO preserves the same trust-region geometry as DPPO while inducing bounded, continuous gradient weights that attenuate diverging updates and provide corrective signals beyond the boundary. Experiments across model scales, architectures, and precision settings show that DRPO improves the stability and efficiency of LLM RL training.