Topology as Experience: Federated Optimization on Collaborations in LLM-based MAS

Topology design for multi-agent systems built on large language models is typically optimized within individual clients, leaving useful collaboration experience from other clients underused. Sharing textual experience introduces growing records and the risk of exposing sensitive task content, while heterogeneous task distributions require client-specific collaboration strategies. To address these limitations, we propose a personalized federated framework that represents collaboration experience as a compact probabilistic topology graph. Specifically, each client combines a shared probabilistic graph that aggregates reusable communication patterns with a personalized probabilistic graph that adapts them to local tasks, while keeping raw tasks and execution traces local. To reduce the cost of topology optimization, a task-conditioned mixture-of-experts predictor learns from historical execution records and supplies inexpensive rewards for probabilistic graph training. Limited real multi-agent feedback then refines the topology policy through reinforcement learning to address the gap between predicted and executed performance. At deployment, the predictor ranks sampled topologies and selects one for execution. Across two heterogeneous three-client suites spanning coding, mathematics, and reasoning, the complete framework achieves the highest mean accuracy in both suites. Predictor pretraining improves the starting topology policy, limited real feedback further refines it, and personalized candidate search reaches 90.0% accuracy with eight candidates in a setting where the shared policy requires 512. These results show how a probabilistic graph turns cross-client collaboration experience into executable, client-adaptive policies.