# A Survey of Reinforcement Learning for Large Reasoning Models

arXiv: https://arxiv.org/abs/2509.08827 · HTML: https://mlsanity.com/paper/2509.08827/

## Key facts

- Cited by 180 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 557 of its 751 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 557)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)

## Built on by (most cited first, 30 of 180)

- [Memory in the Age of AI Agents](https://mlsanity.com/paper/2512.13564/) (2025)
- [Agent0: Unleashing Self-Evolving Agents from Zero Data via Tool-Integrated Reasoning](https://mlsanity.com/paper/2511.16043/) (2025)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)
- [FLEX: Continuous Agent Evolution via Forward Learning from Experience](https://mlsanity.com/paper/2511.06449/) (2025)
- [A Survey of Agentic Reasoning for Large Language Models: Towards Recursively Self-Improving and Collective Agents](https://mlsanity.com/paper/2601.12538/) (2026)
- [BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clipping](https://mlsanity.com/paper/2510.18927/) (2025)
- [Continuum: Efficient and Robust Multi-Turn LLM Agent Scheduling with KV Cache Time-to-Live](https://mlsanity.com/paper/2511.02230/) (2025)
- [FrameThinker: Learning to Think with Long Videos via Multi-Turn Frame Spotlighting](https://mlsanity.com/paper/2509.24304/) (2025)
- [FlowRL: Matching Reward Distributions for LLM Reasoning](https://mlsanity.com/paper/2509.15207/) (2025)
- [Spotlight on Token Perception for Multimodal Reinforcement Learning](https://mlsanity.com/paper/2510.09285/) (2025)
- [Reinforcement Learning Meets Large Language Models: A Survey of Advancements and Applications Across the LLM Lifecycle](https://mlsanity.com/paper/2509.16679/) (2025)
- [Scalable Power Sampling: Unlocking Efficient, Training-Free Reasoning for LLMs via Distribution Sharpening](https://mlsanity.com/paper/2601.21590/) (2026)
- [Beyond Trajectory-Level Attribution: Graph-Based Credit Assignment for Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.26684/) (2026)
- [Demystifying OPD: Length Inflation and Stabilization Strategies for Large Language Models](https://mlsanity.com/paper/2604.08527/) (2026)
- [Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning](https://mlsanity.com/paper/2509.25300/) (2025)
- [Rethinking Entropy Regularization in Large Reasoning Models](https://mlsanity.com/paper/2509.25133/) (2025)
- [Nudging the Boundaries of LLM Reasoning](https://mlsanity.com/paper/2509.25666/) (2025)
- [Reinforcing Chain-of-Thought Reasoning with Self-Evolving Rubrics](https://mlsanity.com/paper/2602.10885/) (2026)
- [STARE-VLA: Progressive Stage-Aware Reinforcement for Fine-Tuning Vision-Language-Action Models](https://mlsanity.com/paper/2512.05107/) (2025)
- [On Predictability of Reinforcement Learning Dynamics for Large Language Models](https://mlsanity.com/paper/2510.00553/) (2025)
- [A Survey on Agentic Multimodal Large Language Models](https://mlsanity.com/paper/2510.10991/) (2025)
- [From Reasoning to Agentic: Credit Assignment in Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2604.09459/) (2026)
- [Knapsack RL: Unlocking Exploration of LLMs via Optimizing Budget Allocation](https://mlsanity.com/paper/2509.25849/) (2025)
- [RewardMap: Tackling Sparse Rewards in Fine-grained Visual Reasoning via Multi-Stage Reinforcement Learning](https://mlsanity.com/paper/2510.02240/) (2025)
- [When Importance Sampling Misallocates Credit: Asymmetric Ratios for Outcome-Supervised RL](https://mlsanity.com/paper/2510.06062/) (2025)
- [Hybrid Reinforcement: When Reward Is Sparse, It's Better to Be Dense](https://mlsanity.com/paper/2510.07242/) (2025)
- [DiFFPO: Training Diffusion LLMs to Reason Fast and Furious via Reinforcement Learning](https://mlsanity.com/paper/2510.02212/) (2025)
- [Rethinking Sample Polarity in Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2512.21625/) (2025)
- [DiffThinker: Towards Generative Multimodal Reasoning with Diffusion Models](https://mlsanity.com/paper/2512.24165/) (2025)

## Abstract (arXiv)

In this paper, we survey recent advances in Reinforcement Learning (RL) for reasoning with Large Language Models (LLMs). RL has achieved remarkable success in advancing the frontier of LLM capabilities, particularly in addressing complex logical tasks such as mathematics and coding. As a result, RL has emerged as a foundational methodology for transforming LLMs into LRMs. With the rapid progress of the field, further scaling of RL for LRMs now faces foundational challenges not only in computational resources but also in algorithm design, training data, and infrastructure. To this end, it is timely to revisit the development of this domain, reassess its trajectory, and explore strategies to enhance the scalability of RL toward Artificial SuperIntelligence (ASI). In particular, we examine research applying RL to LLMs and LRMs for reasoning abilities, especially since the release of DeepSeek-R1, including foundational components, core problems, training resources, and downstream applications, to identify future opportunities and directions for this rapidly evolving area. We hope this review will promote future research on RL for broader reasoning models. Github: https://github.com/TsinghuaC3I/Awesome-RL-for-LRMs