# Compositional RL: Evaluating and Training LLMs for Collaborative Reasoning

arXiv: https://arxiv.org/abs/2610.17456 · HTML: https://mlsanity.com/paper/2610.17456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 75 of its 90 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## 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 75)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [AgentVerse: Facilitating Multi-Agent Collaboration and Exploring Emergent Behaviors](https://mlsanity.com/paper/2308.10848/) (2023)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [ArCHer: Training Language Model Agents via Hierarchical Multi-Turn RL](https://mlsanity.com/paper/2402.19446/) (2024)
- [KernelBench: Can LLMs Write Efficient GPU Kernels?](https://mlsanity.com/paper/2502.10517/) (2025)
- [AI Agents That Matter](https://mlsanity.com/paper/2407.01502/) (2024)
- [Chain of Agents: Large Language Models Collaborating on Long-Context Tasks](https://mlsanity.com/paper/2406.02818/) (2024)
- [Are We Done with MMLU?](https://mlsanity.com/paper/2406.04127/) (2024)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)

## Abstract (arXiv)

Language models are often evaluated alone but increasingly deployed together, routed between, made to debate, ensembled, or collaboratively trained. For a model inside a system, what matters most is not how well it performs on its own, but how much the system gains from its presence. We call this a model's compositional strength and formalize it using the Shapley value of a cooperative game over coalitions of a model pool, and use a model's leave-one-out contribution to the full coalition as a tractable proxy, requiring n+1 rather than 2^n system evaluations. Evaluating individual vs. compositional strengths across five model pools, twelve collaboration methods, and twelve datasets, we find them largely uncorrelated: in 12 of 15 (pool, method-family) settings, individual strength does not translate into compositional advantages, and the coupling is weakest among general-purpose models that practitioners are most likely to deploy. Standalone benchmarks are therefore often poor proxies for models' value in collaborative systems. We then propose compositional reinforcement learning (C-RL), which trains a policy inside a live multi-model system and rewards the outcome produced by the system as a whole, rather than the policy's correctness in isolation. The leave-one-out baseline in Shapley values cancels under a group policy gradient, so this needs no additional rollout cost beyond RL on the collaborative system's outcome and never requires running a coalition without the policy. Across three collaboration protocols and eight tasks spanning reasoning, coding, and scientific discovery, C-RL produces the strongest collaborator in 21 of 24 settings, lifting collaborative performance by +4.0 to +5.4 pts on average (~3x the gain of baselines), up to +13.1 pts.