  Multi-agent reinforcement learning methods have shown remarkable potential in
solving complex multi-agent problems but mostly lack theoretical guarantees.
Recently, mean field control and mean field games have been established as a
tractable solution for large-scale multi-agent problems with many agents. In
this work, driven by a motivating scheduling problem, we consider a
discrete-time mean field control model with common environment states. We
rigorously establish approximate optimality as the number of agents grows in
the finite agent case and find that a dynamic programming principle holds,
resulting in the existence of an optimal stationary policy. As exact solutions
are difficult in general due to the resulting continuous action space of the
limiting mean field Markov decision process, we apply established deep
reinforcement learning methods to solve the associated mean field control
problem. The performance of the learned mean field control policy is compared
to typical multi-agent reinforcement learning approaches and is found to
converge to the mean field performance for sufficiently many agents, verifying
the obtained theoretical results and reaching competitive solutions.
