# Stabilizing Reinforcement Learning with LLMs: Formulation and Practices

arXiv: https://arxiv.org/abs/2512.01374 · HTML: https://mlsanity.com/paper/2512.01374/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Placed in MoE in reinforcement learning and robotics, one of 12 directions in Mixture-of-experts.
- Builds on 8 of its 11 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Placed in

- Mixture-of-experts / [MoE in reinforcement learning and robotics](https://mlsanity.com/moe/moe-in-reinforcement-learning-and-robotics/)

## Builds on (most cited first, 8 of 8)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [Stabilizing MoE Reinforcement Learning by Aligning Training and Inference Routers](https://mlsanity.com/paper/2510.11370/) (2025)
- [Batch size-invariance for policy optimization](https://mlsanity.com/paper/2110.00641/) (2021)

## Built on by (most cited first, 30 of 41)

- [Toward Training Superintelligent Software Agents through Self-Play SWE-RL](https://mlsanity.com/paper/2512.18552/) (2025)
- [Rethinking the Trust Region in LLM Reinforcement Learning](https://mlsanity.com/paper/2602.04879/) (2026)
- [Let It Flow: Agentic Crafting on Rock and Roll, Building the ROME Model within an Open Agentic Learning Ecosystem](https://mlsanity.com/paper/2512.24873/) (2025)
- [Learning to Foresee: Unveiling the Unlocking Efficiency of On-Policy Distillation](https://mlsanity.com/paper/2605.11739/) (2026)
- [Rethinking the Design Space of Reinforcement Learning for Diffusion Models: On the Importance of Likelihood Estimation Beyond Loss Design](https://mlsanity.com/paper/2602.04663/) (2026)
- [PyVision-RL: Forging Open Agentic Vision Models via RL](https://mlsanity.com/paper/2602.20739/) (2026)
- [RLVR without Ineffective Samples: Group Prioritized Off-Policy Optimization for LLM Reasoning](https://mlsanity.com/paper/2606.01281/) (2026)
- [Diagnosing Training Inference Mismatch in LLM Reinforcement Learning via a Zero-Mismatch Reference](https://mlsanity.com/paper/2605.14220/) (2026)
- [Advantage Collapse in Group Relative Policy Optimization: Diagnosis and Mitigation](https://mlsanity.com/paper/2605.21125/) (2026)
- [SeeUPO: Sequence-Level Agentic-RL with Convergence Guarantees](https://mlsanity.com/paper/2602.06554/) (2026)
- [ETS: Energy-Guided Test-Time Scaling for Training-Free RL Alignment](https://mlsanity.com/paper/2601.21484/) (2026)
- [Missing Old Logits in Asynchronous Agentic RL: Semantic Mismatch and Repair Methods for Off-Policy Correction](https://mlsanity.com/paper/2605.12070/) (2026)
- [Rethinking the Divergence Regularization in LLM RL](https://mlsanity.com/paper/2606.09821/) (2026)
- [Stale but Stable: Staleness-Adaptive Trust Regions for Stabilizing Asynchronous Reinforcement Learning](https://mlsanity.com/paper/2607.18722/) (2026)
- [On the Role of Reasoning Patterns in the Generalization Discrepancy of Long Chain-of-Thought Supervised Fine-Tuning](https://mlsanity.com/paper/2604.01702/) (2026)
- [ICRL: Learning to Internalize Self-Critique with Reinforcement Learning](https://mlsanity.com/paper/2605.15224/) (2026)
- [RIFT: Repurposing Negative Samples via Reward-Informed Fine-Tuning](https://mlsanity.com/paper/2601.09253/) (2026)
- [Probing RLVR training instability through the lens of objective-level hacking](https://mlsanity.com/paper/2602.01103/) (2026)
- [Preventing Learning Stagnation in PPO by Scaling to 1 Million Parallel Environments](https://mlsanity.com/paper/2603.06009/) (2026)
- [T2PO: Uncertainty-Guided Exploration Control for Stable Multi-Turn Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.02178/) (2026)
- [ReLibra: Routing-Replay-Guided Load Balancing for MoE Training in Reinforcement Learning](https://mlsanity.com/paper/2605.08639/) (2026)
- [Scaling Reinforcement Learning for Diffusion Models via Velocity Matching](https://mlsanity.com/paper/2608.23664/) (2026)
- [Teaching Thinking Models to Reason with Tools: A Full-Pipeline Recipe for Tool-Integrated Reasoning](https://mlsanity.com/paper/2605.06326/) (2026)
- [Turning Off-Policy Tokens On-Policy: A Plug-in Approach for Improving LLM Alignment](https://mlsanity.com/paper/2607.04728/) (2026)
- [Online Causal Kalman Filtering for Stable and Effective Policy Optimization](https://mlsanity.com/paper/2602.10609/) (2026)
- [Addressing Performance Saturation for LLM RL via Precise Entropy Curve Control](https://mlsanity.com/paper/2604.26326/) (2026)
- [Multi-Step Likelihood-Ratio Correction for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2605.20865/) (2026)
- [Task-Focused Memorization for Multimodal Agents](https://mlsanity.com/paper/2605.31075/) (2026)
- [PR2: Predictive Routing Replay for MoE-Based LLM Reinforcement Learning](https://mlsanity.com/paper/2606.00395/) (2026)
- [OpsLLM: Construction of Large Language Model for Software Operations with Multi-stage Learning](https://mlsanity.com/paper/2605.02906/) (2026)

## Abstract (arXiv)

This paper proposes a novel formulation for reinforcement learning (RL) with large language models, explaining why and under what conditions the true sequence-level reward can be optimized via a surrogate token-level objective in policy gradient methods such as REINFORCE. Specifically, through a first-order approximation, we show that this surrogate becomes increasingly valid only when both the training-inference discrepancy and policy staleness are minimized. This insight provides a principled explanation for the crucial role of several widely adopted techniques in stabilizing RL training, including importance sampling correction, clipping, and particularly Routing Replay for Mixture-of-Experts (MoE) models. Through extensive experiments with a 30B MoE model totaling hundreds of thousands of GPU hours, we show that for on-policy training, the basic policy gradient algorithm with importance sampling correction achieves the highest training stability. When off-policy updates are introduced to accelerate convergence, combining clipping and Routing Replay becomes essential to mitigate the instability caused by policy staleness. Notably, once training is stabilized, prolonged optimization consistently yields comparable final performance regardless of cold-start initialization. We hope that the shared insights and the developed recipes for stable RL training will facilitate future research.