# Interactive Learning for LLM Reasoning

arXiv: https://arxiv.org/abs/2509.26306 · HTML: https://mlsanity.com/paper/2509.26306/

## Key facts

- Cited by 5 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 39 of its 63 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 30 of 39)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [LEVER: Learning to Verify Language-to-Code Generation with Execution](https://mlsanity.com/paper/2302.08468/) (2023)
- [TarMAC: Targeted Multi-Agent Communication](https://mlsanity.com/paper/1810.11187/) (2018)
- [Which Agent Causes Task Failures and When? On Automated Failure Attribution of LLM Multi-Agent Systems](https://mlsanity.com/paper/2505.00212/) (2025)
- [LLM Multi-Agent Systems: Challenges and Open Problems](https://mlsanity.com/paper/2402.03578/) (2024)
- [CPPO: Accelerating the Training of Group Relative Policy Optimization-Based Reasoning Models](https://mlsanity.com/paper/2503.22342/) (2025)
- [Multiagent Finetuning: Self Improvement with Diverse Reasoning Chains](https://mlsanity.com/paper/2501.05707/) (2025)
- [MAPoRL: Multi-Agent Post-Co-Training for Collaborative Large Language Models with Reinforcement Learning](https://mlsanity.com/paper/2502.18439/) (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)
- [Self-Contrast: Better Reflection Through Inconsistent Solving Perspectives](https://mlsanity.com/paper/2401.02009/) (2024)
- [Make Every Penny Count: Difficulty-Adaptive Self-Consistency for Cost-Efficient Reasoning](https://mlsanity.com/paper/2408.13457/) (2024)
- [MARFT: Multi-Agent Reinforcement Fine-Tuning](https://mlsanity.com/paper/2504.16129/) (2025)
- [LLM Collaboration With Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2508.04652/) (2025)

## Built on by (most cited first, 5 of 5)

- [Counterfactual Credit Policy Optimization for Multi-Agent Collaboration](https://mlsanity.com/paper/2603.21563/) (2026)
- [Adaptive Robust Estimator for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2603.21574/) (2026)
- [Experience Sharing in Mutual Reinforcement Learning for Heterogeneous Language Models](https://mlsanity.com/paper/2605.07244/) (2026)
- [AIPO: Learning to Reason from Active Interaction](https://mlsanity.com/paper/2605.08401/) (2026)
- [MAS-Gate: Unlocking Multi-Agent System Lifecycle via Node-Centric Quantification](https://mlsanity.com/paper/2610.17613/) (2026)

## Abstract (arXiv)

Existing multi-agent learning approaches have developed interactive training environments to explicitly promote collaboration among multiple Large Language Models (LLMs), thereby constructing stronger multi-agent systems (MAS). However, during inference, they require re-executing the MAS to obtain final solutions, which diverges from human cognition that individuals can enhance their reasoning capabilities through interactions with others and resolve questions independently in the future. To investigate whether multi-agent interaction can enhance LLMs' independent problem-solving ability, we introduce ILR, a novel co-learning framework for MAS that integrates two key components: Dynamic Interaction and Perception Calibration. Specifically, Dynamic Interaction first adaptively selects either cooperative or competitive strategies depending on question difficulty and model ability. LLMs then exchange information through Idea3, an innovative interaction paradigm designed to mimic human discussion, before deriving their respective final answers. In Perception Calibration, ILR employs Group Relative Policy Optimization (GRPO) to train LLMs while integrating one LLM's reward distribution characteristics into another's reward function, thereby enhancing the cohesion of multi-agent interactions. We evaluate the effectiveness of ILR across three LLMs from two model families of varying scales on five mathematical, one coding, one general question answering, and one scientific reasoning benchmarks. Experimental results show that ILR consistently outperforms single-agent learning, yielding an improvement of up to 5% over the strongest baseline. We further discover that Idea3 can enhance the robustness of stronger LLMs during multi-agent inference, and dynamic interaction types can boost multi-agent learning compared to pure cooperative or competitive strategies.