# Beyond the Stability-Exploration Dilemma: Environmental Regularization for LLM Policy Optimization

arXiv: https://arxiv.org/abs/2608.23311 · HTML: https://mlsanity.com/paper/2608.23311/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 36 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Builds on (most cited first, 24 of 24)

- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Language Models Learn to Mislead Humans via RLHF](https://mlsanity.com/paper/2409.12822/) (2024)
- [Reinforcement and Imitation Learning via Interactive No-Regret Learning](https://mlsanity.com/paper/1406.5979/) (2014)
- [A Survey of Reinforcement Learning Algorithms for Dynamically Varying Environments](https://mlsanity.com/paper/2005.10619/) (2020)
- [Learning Human Objectives by Evaluating Hypothetical Behavior](https://mlsanity.com/paper/1912.05652/) (2019)
- [On-Policy RL with Optimal Reward Baseline](https://mlsanity.com/paper/2505.23585/) (2025)
- [Scalable Reinforcement Post-Training Beyond Static Human Prompts: Evolving Alignment via Asymmetric Self-Play](https://mlsanity.com/paper/2411.00062/) (2024)
- [Align-Pro: A Principled Approach to Prompt Optimization for LLM Alignment](https://mlsanity.com/paper/2501.03486/) (2025)
- [Mitigating Reward Over-Optimization in RLHF via Behavior-Supported Regularization](https://mlsanity.com/paper/2503.18130/) (2025)
- [SALSA: Soup-based Alignment Learning for Stronger Adaptation in RLHF](https://mlsanity.com/paper/2411.01798/) (2024)

## Abstract (arXiv)

Policy optimization (PO) for Large Language Models faces a stability--exploration trade-off, currently mediated by an action-side Policy-KL regularizer. This puts practitioners in a double bind: keeping Policy-KL constrains response behavior and consumes the action-side exploration budget, while dropping it leaves the optimization without an explicit drift control. We argue for an alternative that breaks the dilemma by moving regularization to the input side. As training progresses, the distribution over training queries induced by the current policy drifts unchecked from its pre-RL reference distribution. Concretely, Environment-Regularized Policy Optimization (ERPO) introduces a Query-KL (QKL) term that bounds this query distribution shift, together with a dataset-static reference-derived per-query weight that biases each per-query update toward queries typical under the reference. The QKL gradient flows strictly through the query likelihood; the response score function used by policy-gradient estimators does not appear in the QKL term, so QKL exerts no direct gradient pressure on the response distribution---exploration is preserved. ERPO plugs into GRPO/PPO/REINFORCE-style pipelines without additional forward passes. On six mathematical reasoning benchmarks, ERPO replaces the standard Policy-KL regularizer while achieving effective control over query distribution drift, delivering stronger accuracy and substantially more stable behavior under high-temperature decoding and long-horizon training. Our source code are available at https://github.com/AlibabaResearch/ERPO