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Recently, mean field control (MFC) has provided a tractable and theoreticallyfounded approach to otherwise difficult cooperative multi-agent control.However, the strict assumption of many independent, homogeneous agents may betoo stringent in practice. In this work, we propose a novel discrete-timegeneralization of Markov decision processes and MFC to both many minor agentsand potentially complex major agents -- major-minor mean field control (M3FC).In contrast to deterministic MFC, M3FC allows for stochastic minor agentdistributions with strong correlation between minor agents through the majoragent state, which can model arbitrary problem details not bound to any agent.Theoretically, we give rigorous approximation properties with novel proofs forboth M3FC and existing MFC models in the finite multi-agent problem, togetherwith a dynamic programming principle for solving such problems. In theinfinite-horizon discounted case, existence of an optimal stationary policyfollows. Algorithmically, we propose the major-minor mean field proximal policyoptimization algorithm (M3FPPO) as a novel multi-agent reinforcement learningalgorithm and demonstrate its success in illustrative M3FC-type problems.

Multi-Agent Reinforcement Learning via Mean Field Control: Common Noise, Major Agents and Approximation Properties