Networked Communication for Decentralised Cooperative Agents in Mean-Field Control

Abstract

The mean-field framework has been used to find approximate solutions to problems involving very large populations of symmetric, anonymous agents, which may be intractable by other methods. The cooperative mean-field control (MFC) problem has received less attention than the non-cooperative mean-field game (MFG), despite the former potentially being more useful as a tool for engineering large-scale collective behaviours. Decentralised communication algorithms have recently been introduced to MFGs, giving benefits to learning speed and robustness. Inspired by this, we introduce networked communication to MFC - where populations arguably have broader incentive to communicate - and in particular to the setting where decentralised agents learn online from a single, non-episodic run of the empirical system. We adapt recent MFG algorithms to this new setting, as well as contributing a novel sub-routine allowing networked agents to estimate the global average reward from their local neighbourhood. Previous theoretical analysis of decentralised communication in MFGs does not extend trivially to MFC. We therefore contribute new theory proving that in MFC the networked communication scheme allows agents to increase social welfare faster than under both of the two typical alternative architectures, namely independent and centralised learning. We provide experiments that support this new result across different classes of cooperative game, and also give numerous ablation studies and additional experiments concerning numbers of communication round and robustness to communication failures.