Training Small LLMs as Spatial Multi-Agent Policies
Authors: Yi Mao, Andrew Perrault
Organizations: Department of Computer Science and Engineering, The Ohio State University
Abstract
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.
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.
Effective training-time guidance is central to multi-agent reinforcement learning (MARL), yet remains difficult in sparse-reward settings where weak supervision limits coordination and policy improvement, and existing methods often require substantial domain expertise or manual design effort. Large language models (LLMs) provide a promising alternative for flexible learning-signal design, yet existing LLM-based methods remain largely single-agent-oriented, one-shot, or weakly validated for the evolving training dynamics of cooperative MARL. To address these limitations, we propose LLM-ALSO, an iterative LLM-driven adaptive learning-signal optimization framework for MARL. Rather than directly deploying LLM-generated rewards, LLM-ALSO decomposes adaptation into iterative diagnosis, proposal, and validation: a Critic LLM diagnoses stage-specific learning and coordination failures from sparse-return metrics and compact behavior evidence, a Generator LLM proposes candidate reward-shaping configurations conditioned on the diagnosis, and branch-validation feedback refines candidates before they affect the main training trajectory. Through short-horizon validation and stage-aware adaptation, LLM-ALSO promotes only validated updates into training, reducing the risk of unreliable LLM-generated modifications. Experiments on sparse-reward cooperative MARL tasks show that LLM-ALSO improves sparse-evaluation performance and learning efficiency.
Multi-agent LLM systems have shown promise for complex reasoning, yet recent evaluations reveal they often underperform single-model baselines. We identify a structural failure mode in sequential fine-tuning of shared-context teams: updating one agent shifts the team's context distribution, and when subsequent updates are evaluated on cached rollouts, this mismatch compounds. We formalize this as the compounding occupancy shift and prove that stale-occupancy evaluation incurs a penalty that scales quadratically with the number of agents. In contrast, intermediate-occupancy evaluation reduces this to linear scaling. We propose TeamTR, a trust-region framework that resamples trajectories after each component update and enforces per-agent divergence control, yielding rigorous per-update and per-stage improvement lower bounds. Experiments show that TeamTR outperforms single-agent and sequential baselines with 7.1% on average, mitigates coordination regressions, and supports plug-and-play component replacement. Code is available at https://github.com/Yydc/TeamTR.