# SAGE: Multi-Agent Self-Evolution for LLM Reasoning

arXiv: https://arxiv.org/abs/2603.15255 · HTML: https://mlsanity.com/paper/2603.15255/

## Key facts

- Cited by 6 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 34 of its 41 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## 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 / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 30 of 34)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [A Comprehensive Survey of Self-Evolving AI Agents: A New Paradigm Bridging Foundation Models and Lifelong Agentic Systems](https://mlsanity.com/paper/2508.07407/) (2025)
- [A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence](https://mlsanity.com/paper/2507.21046/) (2025)
- [WebAgent-R1: Training Web Agents via End-to-End Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2505.16421/) (2025)
- [EvolveR: Self-Evolving LLM Agents through an Experience-Driven Lifecycle](https://mlsanity.com/paper/2510.16079/) (2025)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [AgentEvolver: Towards Efficient Self-Evolving Agent System](https://mlsanity.com/paper/2511.10395/) (2025)
- [ReMA: Learning to Meta-think for LLMs with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2503.09501/) (2025)
- [MALT: Improving Reasoning with Multi-Agent LLM Training](https://mlsanity.com/paper/2412.01928/) (2024)
- [Agent0: Unleashing Self-Evolving Agents from Zero Data via Tool-Integrated Reasoning](https://mlsanity.com/paper/2511.16043/) (2025)
- [LLM-based Multi-Agent Reinforcement Learning: Current and Future Directions](https://mlsanity.com/paper/2405.11106/) (2024)
- [Multi-Agent Evolve: LLM Self-Improve through Co-evolution](https://mlsanity.com/paper/2510.23595/) (2025)
- [MARFT: Multi-Agent Reinforcement Fine-Tuning](https://mlsanity.com/paper/2504.16129/) (2025)
- [Stronger-MAS: Multi-Agent Reinforcement Learning for Collaborative LLMs](https://mlsanity.com/paper/2510.11062/) (2025)

## Built on by (most cited first, 6 of 6)

- [From Question Answering to Task Completion: A Survey on Agent System and Harness Design](https://mlsanity.com/paper/2606.20683/) (2026)
- [Instructing LLMs to Negotiate using Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2604.09855/) (2026)
- [EVE-Agent: Evidence-Verifiable Self-Evolving Agents](https://mlsanity.com/paper/2605.22905/) (2026)
- [MAGE: Multi-Agent Self-Evolution with Co-Evolutionary Knowledge Graphs](https://mlsanity.com/paper/2605.10064/) (2026)
- [MetaRSI / RSI2: A Meta-Recursive Self-Improving System for Recursive Self-Improving Systems Themselves](https://mlsanity.com/paper/2609.06396/) (2026)
- [MetaResearcher: Scaling Deep Research via Self-Reflective Reinforcement Learning in Adversarial Virtual Environments](https://mlsanity.com/paper/2606.19893/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards improves reasoning in large language models (LLMs), but many methods still rely on large human-labeled datasets. While self-play reduces this dependency, it often lacks explicit planning and strong quality control, limiting stability in long-horizon multi-step reasoning. We present SAGE (Self-evolving Agents for Generalized reasoning Evolution), a closed-loop framework where four agents: Challenger, Planner, Solver, and Critic, co-evolve from a shared LLM backbone using only a small seed set. The Challenger continuously generates increasingly difficult tasks; the Planner converts each task into a structured multi-step plan; and the Solver follows the plan to produce an answer, whose correctness is determined by external verifiers. The Critic scores and filters both generated questions and plans to prevent curriculum drift and maintain training signal quality, enabling stable self-training. Across mathematics and code-generation benchmarks, SAGE delivers consistent gains across model scales, improving the Qwen-2.5-7B model by 8.9% on LiveCodeBench and 10.7% on OlympiadBench.