  Multi-agent reinforcement learning has been successfully applied to a number
of challenging problems. Despite these empirical successes, theoretical
understanding of different algorithms is lacking, primarily due to the curse of
dimensionality caused by the exponential growth of the state-action space with
the number of agents. We study a fundamental problem of multi-agent linear
quadratic regulator (LQR) in a setting where the agents are partially
exchangeable. In this setting, we develop a hierarchical actor-critic
algorithm, whose computational complexity is independent of the total number of
agents, and prove its global linear convergence to the optimal policy. As LQRs
are often used to approximate general dynamic systems, this paper provides an
important step towards a better understanding of general hierarchical
mean-field multi-agent reinforcement learning.
