Marginal-Contribution Policy Gradients under Filtered Feedback for Multi-Agent LLMs

Large Language Models (LLMs) in multi-agent systems (MAS) have shown promise for complex tasks, yet current training methods lack principled ways to connect system-level evaluation with agent- and message-level learning. We propose a theoretical framework that unifies cooperative game-theoretic attribution with process reward modeling to transform system evaluation to agent credit to response-level signals. Unlike prior approaches that rely only on attribution (Shapley) or step-level labels (PRM), our method produces local, signed, and credit-conserving signals. In success cases, Shapley-based credit assignment fairly allocates outcomes across agents and is refined into per-message rewards that promote cooperation while discouraging redundancy or sabotage; in failure cases, first-error localization yields repair-aware preferences that penalize harmful steps while rewarding corrective attempts. The resulting signals are bounded, cooperative, and directly compatible with reinforcement- or preference-based post-training, providing a unified and auditable pathway from global evaluation to local supervision in LLM multi-agent training. Our contribution is conceptual: we present a theoretical foundation and training signals, leaving empirical validation for future work.

Multi-agent systems (MAS) built on large language models (LLMs) provide a promising framework for solving complex tasks through role specialization and structured interaction. However, their performance is often limited by miscoordination and, more fundamentally, the lack of fine-grained credit assignment across agents. Existing approaches typically rely on coarse-grained feedback, making it difficult to identify which agents or interaction steps are responsible for errors. We propose Gradient-Based Connections (GBC), an approach for fine-grained attribution and optimization of multi-agent systems. GBC models a MAS as a computational graph and introduces gradient-based connection weights to quantify the influence of each agent's output on downstream agents at the token level. By constructing an attribution graph and propagating task-specific loss signals backward, our method enables precise identification of error sources and targeted prompt optimization. We further develop AgentChord, an efficient implementation that leverages prefix-based gradient computation. Experiments on MultiWOZ and τ-bench show that GBC improves multi-agent performance and outperforms strong single-agent and multi-agent baselines, and higher attribution quality is associated with greater optimization effectiveness. Code is available at: https://github.com/yxc-cyber/AgentChord.

Training LLM-based multi-agent systems with multi-agent reinforcement learning is rapidly gaining traction, and a parallel line of work argues that such systems should be judged by their behavior, not only their reward. We take up both threads in spatial cooperative games, where small frozen LLMs prompted with low-level actions fail outright, earning zero reward. Guided by the options/semi-MDP framework---and, because option execution is asynchronous across agents, its multi-agent extension in macro-action Dec-POMDPs---we equip each game with a library of symbolic \emph{options}: typed, state-feasible, short-horizon behaviors executed by a symbolic planner. Each library is drafted by a frontier coding model from the game's source code; the feasibility guards that filter each menu are then synthesized mechanically from cheap random-policy burn-in rollouts---a guard is adopted only if it explains repeated execution failures while hiding no logged success---so no guard is authored, selected, or reward-tuned by hand. Each agent's LLM acts as its policy over options, with a private per-agent LoRA adapter trained by a per-agent variant of multi-agent GRPO (PA-MAGRPO); this lifts frozen bases from zero reward to competent play across three games and four small backbones. Behavioral audits then reveal that reward and cooperation decouple: a rising reward curve may simply mean that one agent has learned to run the entire task alone while its partner idles---cooperation emerges only when the task makes it necessary. Reward alone is thus an unreliable readout of cooperation; behavioral evaluation must sit alongside it.