Connectivity-Influence Weighting: A Structural Bias for Graph-Based MARL

Coordinating autonomous agents in Multi-Agent Reinforcement Learning (MARL) is hindered by challenges of scalability and effective information sharing, particularly in partially observable environments. While Graph Neural Networks (GNNs) model agent interactions, they often fail to leverage network structure, treating all connections as equally important. This paper introduces Connectivity-Influence Weighting (CIW), a mechanism that injects a structural inductive bias into the message-passing pipeline. CIW dynamically modulates message importance based on node connectivity, allowing agents to prioritize information from either highly connected or peripheral neighbors through two modes: Hub-Weighted (HW) and Fringe-Weighted (FW). We integrate CIW into a Transformer-based GNN with a decentralized actor–centralized critic architecture. Empirical evaluation on navigation tasks across varying agent densities shows that HW excels in sparse settings, while FW is superior in dense ones. CIW-enhanced models consistently outperform a graph-based baseline and approach oracle performance, highlighting the value of structurally guided information filtering for scalable and robust multi-agent coordination.