Stabilizing Reinforcement Learning with LLMs: Formulation and Practices
On the map: Mixture-of-experts → MoE in reinforcement learning and robotics
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.
Key facts. Cited by 38 papers in the map (data through 7 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.
Builds on
8 of 11 references.
Closest ancestors · 2
Same direction, newest first
- 2025Stabilizing MoE Reinforcement Learning by Aligning Training and Inference Routers13 Oct
- 2025MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention16 Jun
Other references · 6
- 2017Proximal Policy Optimization Algorithmscited by 14,441
- 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 8,851
- 2025Qwen3 Technical Reportcited by 8,195
- 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,146
- 2025Understanding R1-Zero-Like Training: A Critical Perspectivecited by 1,276
- 2021Batch size-invariance for policy optimizationcited by 33
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Citing papers per year: 2025: 2; 2026: 36.
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- 2025Toward Training Superintelligent Software Agents through Self-Play SWE-RLcited by 37
- 2026Rethinking the Trust Region in LLM Reinforcement Learningcited by 32
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- 2026SeeUPO: Sequence-Level Agentic-RL with Convergence Guaranteescited by 6
- 2026Diagnosing Training Inference Mismatch in LLM Reinforcement Learning via a Zero-Mismatch Referencecited by 5
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- 2026On the Role of Reasoning Patterns in the Generalization Discrepancy of Long Chain-of-Thought Supervised Fine-Tuningcited by 4
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- 2026Probing RLVR training instability through the lens of objective-level hackingcited by 3
- 2026Preventing Learning Stagnation in PPO by Scaling to 1 Million Parallel Environmentscited by 3
- 2026ICRL: Learning to Internalize Self-Critique with Reinforcement Learningcited by 3
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- 2026ReLibra: Routing-Replay-Guided Load Balancing for MoE Training in Reinforcement Learningcited by 2
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- 2026T2PO: Uncertainty-Guided Exploration Control for Stable Multi-Turn Agentic Reinforcement Learningcited by 1
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- 2026ARMOR: Stabilizing On-Policy LLM RL with Off-Policy Anchor Samples11 Jul 2026
- 2026Turning Off-Policy Tokens On-Policy: A Plug-in Approach for Improving LLM Alignment6 Jul 2026
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26 more
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- 2026PR2: Predictive Routing Replay for MoE-Based LLM Reinforcement Learning29 May 2026
- 2026Task-Focused Memorization for Multimodal Agents29 May 2026
- 2026Advantage Collapse in Group Relative Policy Optimization: Diagnosis and Mitigation20 May 2026
- 2026Multi-Step Likelihood-Ratio Correction for Reinforcement Learning with Verifiable Rewards20 May 2026
- 2026Diagnosing Training Inference Mismatch in LLM Reinforcement Learning via a Zero-Mismatch Reference14 May 2026
- 2026ICRL: Learning to Internalize Self-Critique with Reinforcement Learning13 May 2026
- 2026Missing Old Logits in Asynchronous Agentic RL: Semantic Mismatch and Repair Methods for Off-Policy Correction12 May 2026
- 2026ReLibra: Routing-Replay-Guided Load Balancing for MoE Training in Reinforcement Learning9 May 2026
- 2026Teaching Thinking Models to Reason with Tools: A Full-Pipeline Recipe for Tool-Integrated Reasoning7 May 2026
- 2026T2PO: Uncertainty-Guided Exploration Control for Stable Multi-Turn Agentic Reinforcement Learning4 May 2026
- 2026Addressing Performance Saturation for LLM RL via Precise Entropy Curve Control29 Apr 2026
- 2026OpsLLM: Construction of Large Language Model for Software Operations with Multi-stage Learning6 Apr 2026
- 2026On the Role of Reasoning Patterns in the Generalization Discrepancy of Long Chain-of-Thought Supervised Fine-Tuning2 Apr 2026
- 2026Preventing Learning Stagnation in PPO by Scaling to 1 Million Parallel Environments6 Mar 2026
- 2026PyVision-RL: Forging Open Agentic Vision Models via RL24 Feb 2026
- 2026Online Causal Kalman Filtering for Stable and Effective Policy Optimization11 Feb 2026
- 2026SeeUPO: Sequence-Level Agentic-RL with Convergence Guarantees6 Feb 2026
- 2026Rethinking the Trust Region in LLM Reinforcement Learning4 Feb 2026
- 2026Rethinking the Design Space of Reinforcement Learning for Diffusion Models: On the Importance of Likelihood Estimation Beyond Loss Design4 Feb 2026
- 2026Probing RLVR training instability through the lens of objective-level hacking1 Feb 2026
- 2026ETS: Energy-Guided Test-Time Scaling for Training-Free RL Alignment29 Jan 2026
- 2026RIFT: Repurposing Negative Samples via Reward-Informed Fine-Tuning14 Jan 2026
- 2025Let It Flow: Agentic Crafting on Rock and Roll, Building the ROME Model within an Open Agentic Learning Ecosystem31 Dec 2025
- 2025Toward Training Superintelligent Software Agents through Self-Play SWE-RL21 Dec 2025
- 2026Rethinking the Trust Region in LLM Reinforcement Learningcited by 32
- 2026Rethinking the Design Space of Reinforcement Learning for Diffusion Models: On the Importance of Likelihood Estimation Beyond Loss Designcited by 17
- 2026Advantage Collapse in Group Relative Policy Optimization: Diagnosis and Mitigationcited by 7
- 2026RLVR without Ineffective Samples: Group Prioritized Off-Policy Optimization for LLM Reasoningcited by 7
- 2026Rethinking the Divergence Regularization in LLM RLcited by 5
- 2026On the Role of Reasoning Patterns in the Generalization Discrepancy of Long Chain-of-Thought Supervised Fine-Tuningcited by 4
- 2026ETS: Energy-Guided Test-Time Scaling for Training-Free RL Alignmentcited by 3
- 2026Probing RLVR training instability through the lens of objective-level hackingcited by 3
- 2026Teaching Thinking Models to Reason with Tools: A Full-Pipeline Recipe for Tool-Integrated Reasoningcited by 2
- 2026T2PO: Uncertainty-Guided Exploration Control for Stable Multi-Turn Agentic Reinforcement Learningcited by 1
- 2026Multi-Step Likelihood-Ratio Correction for Reinforcement Learning with Verifiable Rewardscited by 1
- 2026Addressing Performance Saturation for LLM RL via Precise Entropy Curve Controlcited by 0
12 most cited of 16 All 16 (JSON)
- 2026Rethinking Training-Inference Mismatch in LLM Reinforcement Learning: Where It Arises and How to Correct It26 Sep 2026
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- 2026ARMOR: Stabilizing On-Policy LLM RL with Off-Policy Anchor Samples11 Jul 2026
- 2026A Gradient Perspective on RLVR Stability and Winner Advantage Policy Optimization15 Jun 2026
- 2026Rethinking the Divergence Regularization in LLM RL8 Jun 2026
- 2026RLVR without Ineffective Samples: Group Prioritized Off-Policy Optimization for LLM Reasoning31 May 2026
- 2026Advantage Collapse in Group Relative Policy Optimization: Diagnosis and Mitigation20 May 2026
- 2026Multi-Step Likelihood-Ratio Correction for Reinforcement Learning with Verifiable Rewards20 May 2026
- 2026Teaching Thinking Models to Reason with Tools: A Full-Pipeline Recipe for Tool-Integrated Reasoning7 May 2026
- 2026T2PO: Uncertainty-Guided Exploration Control for Stable Multi-Turn Agentic Reinforcement Learning4 May 2026
- 2026Addressing Performance Saturation for LLM RL via Precise Entropy Curve Control29 Apr 2026
- 2026On the Role of Reasoning Patterns in the Generalization Discrepancy of Long Chain-of-Thought Supervised Fine-Tuning2 Apr 2026
12 newest of 16 All 16 (JSON)
- 2025Toward Training Superintelligent Software Agents through Self-Play SWE-RLcited by 37
- 2025Let It Flow: Agentic Crafting on Rock and Roll, Building the ROME Model within an Open Agentic Learning Ecosystemcited by 28
- 2026PyVision-RL: Forging Open Agentic Vision Models via RLcited by 14
- 2026SeeUPO: Sequence-Level Agentic-RL with Convergence Guaranteescited by 6
- 2026Missing Old Logits in Asynchronous Agentic RL: Semantic Mismatch and Repair Methods for Off-Policy Correctioncited by 4
- 2026ICRL: Learning to Internalize Self-Critique with Reinforcement Learningcited by 3
- 2026Task-Focused Memorization for Multimodal Agentscited by 1
- 2026Task-Focused Memorization for Multimodal Agents29 May 2026
- 2026ICRL: Learning to Internalize Self-Critique with Reinforcement Learning13 May 2026
- 2026Missing Old Logits in Asynchronous Agentic RL: Semantic Mismatch and Repair Methods for Off-Policy Correction12 May 2026
- 2026PyVision-RL: Forging Open Agentic Vision Models via RL24 Feb 2026
- 2026SeeUPO: Sequence-Level Agentic-RL with Convergence Guarantees6 Feb 2026
- 2025Let It Flow: Agentic Crafting on Rock and Roll, Building the ROME Model within an Open Agentic Learning Ecosystem31 Dec 2025
- 2025Toward Training Superintelligent Software Agents through Self-Play SWE-RL21 Dec 2025
- 2026Stale but Stable: Staleness-Adaptive Trust Regions for Stabilizing Asynchronous Reinforcement Learningcited by 5
- 2026ReLibra: Routing-Replay-Guided Load Balancing for MoE Training in Reinforcement Learningcited by 2
- 2026PR2: Predictive Routing Replay for MoE-Based LLM Reinforcement Learningcited by 1
- 2026Stale but Stable: Staleness-Adaptive Trust Regions for Stabilizing Asynchronous Reinforcement Learning21 Jul 2026
- 2026PR2: Predictive Routing Replay for MoE-Based LLM Reinforcement Learning29 May 2026
- 2026ReLibra: Routing-Replay-Guided Load Balancing for MoE Training in Reinforcement Learning9 May 2026
- 2026Diagnosing Training Inference Mismatch in LLM Reinforcement Learning via a Zero-Mismatch Referencecited by 5
- 2026Preventing Learning Stagnation in PPO by Scaling to 1 Million Parallel Environmentscited by 3
- 2026Online Causal Kalman Filtering for Stable and Effective Policy Optimizationcited by 1
- 2026OpsLLM: Construction of Large Language Model for Software Operations with Multi-stage Learningcited by 0
- 2026Reformulate LLM Reinforcement Learning for Efficient Training under Black-box Discrepancycited by 0
- 2026LLM Evolution as an Industry-Scale Ecosystem: A Lifecycle Perspective on Continual Learningcited by 0
- 2026Predictive Divergence Masks for LLM RLcited by 0
- 2026DualSQL: Text-to-SQL with Multi-Agent Reinforcement Learningcited by 0
- 2026A Pinch of SFT, A Dash of RL: When Reinforcement Learning Helps Long-Horizon Advertising Agentscited by 0
- 2026DualSQL: Text-to-SQL with Multi-Agent Reinforcement Learning16 Sep 2026
- 2026A Pinch of SFT, A Dash of RL: When Reinforcement Learning Helps Long-Horizon Advertising Agents29 Aug 2026
- 2026Predictive Divergence Masks for LLM RL12 Jul 2026
- 2026LLM Evolution as an Industry-Scale Ecosystem: A Lifecycle Perspective on Continual Learning12 Jun 2026
- 2026Reformulate LLM Reinforcement Learning for Efficient Training under Black-box Discrepancy7 Jun 2026
- 2026Diagnosing Training Inference Mismatch in LLM Reinforcement Learning via a Zero-Mismatch Reference14 May 2026
- 2026OpsLLM: Construction of Large Language Model for Software Operations with Multi-stage Learning6 Apr 2026
- 2026Preventing Learning Stagnation in PPO by Scaling to 1 Million Parallel Environments6 Mar 2026
- 2026Online Causal Kalman Filtering for Stable and Effective Policy Optimization11 Feb 2026
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