Compositional RL: Evaluating and Training LLMs for Collaborative Reasoning

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.