# Long-Horizon RL Needs Muon

arXiv: https://arxiv.org/abs/2610.20256 · HTML: https://mlsanity.com/paper/2610.20256/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Training Software Engineering Agents and Verifiers with SWE-Gym](https://mlsanity.com/paper/2412.21139/) (2024)
- [SWE-smith: Scaling Data for Software Engineering Agents](https://mlsanity.com/paper/2504.21798/) (2025)
- [R2E-Gym: Procedural Environments and Hybrid Verifiers for Scaling Open-Weights SWE Agents](https://mlsanity.com/paper/2504.07164/) (2025)
- [Stabilizing Reinforcement Learning with LLMs: Formulation and Practices](https://mlsanity.com/paper/2512.01374/) (2025)
- [Single-Rollout Asynchronous Optimization for Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.07508/) (2026)
- [SWE-World: Building Software Engineering Agents in Docker-Free Environments](https://mlsanity.com/paper/2602.03419/) (2026)
- [SWE-Master: Unleashing the Potential of Software Engineering Agents via Post-Training](https://mlsanity.com/paper/2602.03411/) (2026)
- [ARLArena: A Unified Framework for Stable Agentic Reinforcement Learning](https://mlsanity.com/paper/2602.21534/) (2026)
- [Stable Asynchrony: Variance-Controlled Off-Policy RL for LLMs](https://mlsanity.com/paper/2602.17616/) (2026)
- [Stabilizing Off-Policy Training for Long-Horizon LLM Agent via Turn-Level Importance Sampling and Clipping-Triggered Normalization](https://mlsanity.com/paper/2511.20718/) (2025)
- [Demystifying Reinforcement Learning for Long-Horizon Tool-Using Agents: A Comprehensive Recipe](https://mlsanity.com/paper/2603.21972/) (2026)
- [Rethinking Muon Beyond Pretraining: Spectral Failures and High-Pass Remedies for VLA and RLVR](https://mlsanity.com/paper/2605.19282/) (2026)
- [Balanced Aggregation: Understanding and Fixing Aggregation Bias in GRPO](https://mlsanity.com/paper/2605.04077/) (2026)
- [Reward Engineering for Software Tasks: A Survey of Reinforcement Learning Approaches](https://mlsanity.com/paper/2601.19100/) (2026)
- [SPO++: Stream-Aligned Policy Optimization for Asynchronous Agentic RL](https://mlsanity.com/paper/2608.24870/) (2026)
- [When Does Muon Help Agentic Reinforcement Learning?](https://mlsanity.com/paper/2607.16169/) (2026)

## Abstract (arXiv)

Long-horizon agents must coordinate reasoning, tool use, and environment feedback over extended interactions. Learning from sparse outcome rewards requires weighting trajectories of different lengths and updating the policy while rollouts are still being collected. We examine a single-rollout asynchronous recipe combining Muon, token-averaged loss, truncated importance sampling, and auxiliary length and tool-error penalties. Single-rollout sampling allows asynchronous learning without waiting for multiple trajectories for the same issue. We study optimizer choices and recipe components for repository-level issue resolution across two model families. The evaluated training runs show higher training success with the full recipe than with the baselines.