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Learning in multi-agent systems is highly challenging due to several factorsincluding the non-stationarity introduced by agents' interactions and thecombinatorial nature of their state and action spaces. In particular, weconsider the Mean-Field Control (MFC) problem which assumes an asymptoticallyinfinite population of identical agents that aim to collaboratively maximizethe collective reward. In many cases, solutions of an MFC problem are goodapproximations for large systems, hence, efficient learning for MFC is valuablefor the analogous discrete agent setting with many agents. Specifically, wefocus on the case of unknown system dynamics where the goal is tosimultaneously optimize for the rewards and learn from experience. We proposean efficient model-based reinforcement learning algorithm, $M^3-UCRL$, thatruns in episodes, balances between exploration and exploitation during policylearning, and provably solves this problem. Our main theoretical contributionsare the first general regret bounds for model-based reinforcement learning forMFC, obtained via a novel mean-field type analysis. To learn the system'sdynamics, $M^3-UCRL$ can be instantiated with various statistical models, e.g.,neural networks or Gaussian Processes. Moreover, we provide a practicalparametrization of the core optimization problem that facilitatesgradient-based optimization techniques when combined with differentiabledynamics approximation methods such as neural networks.

Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learning