# Agent RL Scaling Law: Agent RL with Spontaneous Code Execution for Mathematical Problem Solving

arXiv: https://arxiv.org/abs/2505.07773 · HTML: https://mlsanity.com/paper/2505.07773/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 23 of its 30 references that are in the map.
- First posted on arXiv 12 May 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 23 of 23)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [R1-Searcher: Incentivizing the Search Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2503.05592/) (2025)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Tool Learning with Large Language Models: A Survey](https://mlsanity.com/paper/2405.17935/) (2024)
- [ToRL: Scaling Tool-Integrated RL](https://mlsanity.com/paper/2503.23383/) (2025)
- [MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2310.03731/) (2023)
- [Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models](https://mlsanity.com/paper/2503.21380/) (2025)
- [Does RLHF Scale? Exploring the Impacts From Data, Model, and Method](https://mlsanity.com/paper/2412.06000/) (2024)

## Built on by (most cited first, 30 of 62)

- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [WebDancer: Towards Autonomous Information Seeking Agency](https://mlsanity.com/paper/2505.22648/) (2025)
- [Agentic Reinforced Policy Optimization](https://mlsanity.com/paper/2507.19849/) (2025)
- [SimpleTIR: End-to-End Reinforcement Learning for Multi-Turn Tool-Integrated Reasoning](https://mlsanity.com/paper/2509.02479/) (2025)
- [A Survey of Context Engineering for Large Language Models](https://mlsanity.com/paper/2507.13334/) (2025)
- [Mini-o3: Scaling Up Reasoning Patterns and Interaction Turns for Visual Search](https://mlsanity.com/paper/2509.07969/) (2025)
- [VerlTool: Towards Holistic Agentic Reinforcement Learning with Tool Use](https://mlsanity.com/paper/2509.01055/) (2025)
- [Chain-of-Agents: End-to-End Agent Foundation Models via Multi-Agent Distillation and Agentic RL](https://mlsanity.com/paper/2508.13167/) (2025)
- [In-the-Flow Agentic System Optimization for Effective Planning and Tool Use](https://mlsanity.com/paper/2510.05592/) (2025)
- [Training-Free Group Relative Policy Optimization](https://mlsanity.com/paper/2510.08191/) (2025)
- [rStar2-Agent: Agentic Reasoning Technical Report](https://mlsanity.com/paper/2508.20722/) (2025)
- [AutoTIR: Autonomous Tools Integrated Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2507.21836/) (2025)
- [Demystifying Reinforcement Learning in Agentic Reasoning](https://mlsanity.com/paper/2510.11701/) (2025)
- [Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning](https://mlsanity.com/paper/2509.25300/) (2025)
- [Flash-Searcher: Fast and Effective Web Agents via DAG-Based Parallel Execution](https://mlsanity.com/paper/2509.25301/) (2025)
- [Towards Effective Code-Integrated Reasoning](https://mlsanity.com/paper/2505.24480/) (2025)
- [RLFactory: A Plug-and-Play Reinforcement Learning Post-Training Framework for LLM Multi-Turn Tool-Use](https://mlsanity.com/paper/2509.06980/) (2025)
- [Don't Just Fine-tune the Agent, Tune the Environment](https://mlsanity.com/paper/2510.10197/) (2025)
- [AgentMath: Empowering Mathematical Reasoning for Large Language Models via Tool-Augmented Agent](https://mlsanity.com/paper/2512.20745/) (2025)
- [CoRT: Code-integrated Reasoning within Thinking](https://mlsanity.com/paper/2506.09820/) (2025)
- [DraCo: Draft as CoT for Text-to-Image Preview and Rare Concept Generation](https://mlsanity.com/paper/2512.05112/) (2025)
- [Learn the Ropes, Then Trust the Wins: Self-imitation with Progressive Exploration for Agentic Reinforcement Learning](https://mlsanity.com/paper/2509.22601/) (2025)
- [Scaling Generalist Data-Analytic Agents](https://mlsanity.com/paper/2509.25084/) (2025)
- [AutoTool: Dynamic Tool Selection and Integration for Agentic Reasoning](https://mlsanity.com/paper/2512.13278/) (2025)
- [Memory-T1: Reinforcement Learning for Temporal Reasoning in Multi-session Agents](https://mlsanity.com/paper/2512.20092/) (2025)
- [Safe and Scalable Web Agent Learning via Recreated Websites](https://mlsanity.com/paper/2603.10505/) (2026)
- [ReSeek: A Self-Correcting Framework for Search Agents with Instructive Rewards](https://mlsanity.com/paper/2510.00568/) (2025)
- [MTIR-SQL: Multi-turn Tool-Integrated Reasoning Reinforcement Learning for Text-to-SQL](https://mlsanity.com/paper/2510.25510/) (2025)
- [CuES: A Curiosity-driven and Environment-grounded Synthesis Framework for Agentic RL](https://mlsanity.com/paper/2512.01311/) (2025)
- [DatasetResearch: Benchmarking Agent Systems for Demand-Driven Dataset Discovery](https://mlsanity.com/paper/2508.06960/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) often struggle with mathematical reasoning tasks requiring precise, verifiable computation. While Reinforcement Learning (RL) from outcome-based rewards enhances text-based reasoning, understanding how agents autonomously learn to leverage external tools like code execution remains crucial. We investigate RL from outcome-based rewards for Tool-Integrated Reasoning, ZeroTIR, training base LLMs to spontaneously generate and execute Python code for mathematical problems without supervised tool-use examples. Our central contribution is we demonstrate that as RL training progresses, key metrics scale predictably. Specifically, we observe strong positive correlations where increased training steps lead to increases in the spontaneous code execution frequency, the average response length, and, critically, the final task accuracy. This suggests a quantifiable relationship between computational effort invested in training and the emergence of effective, tool-augmented reasoning strategies. We implement a robust framework featuring a decoupled code execution environment and validate our findings across standard RL algorithms and frameworks. Experiments show ZeroTIR significantly surpasses non-tool ZeroRL baselines on challenging math benchmarks. Our findings provide a foundational understanding of how autonomous tool use is acquired and scales within Agent RL, offering a reproducible benchmark for future studies. Code is released at hrefhttps://github.com/yyht/openrlhfasyncpiplinehttps://github.com/yyht/openrlhfasyncpipline.