Graphon Mean-Field Control for Cooperative Multi-Agent Reinforcement Learning

Multi-agent reinforcement learning (MARL) has found various applications in the field of transportation and simulating [50, 1], stock price analyzing and trading [32, 31], wireless communication networks [12, 11, 13], and learning behaviors in social dilemmas [33, 28, 34]. MARL, however, becomes intractable due to the complex interactions among agents as the number of agents increases. A recent tractable approach is a mean-field approach by considering MARL in the regime with a large number of homogeneous agents under weak interactions [20]. According to the number of agents and learning goals, there are three subtle types of mean-field theories for MARL. The first one is called mean-field MARL (MF-MARL), which refers to the empirical average of the states or actions of a finite population. For example, [52] proposes to approximate interactions within the population of agents by averaging the actions of the overall population or neighboring agents.