  We investigate reinforcement learning for mean field control problems in
discrete time, which can be viewed as Markov decision processes for a large
number of exchangeable agents interacting in a mean field manner. Such problems
arise, for instance when a large number of robots communicate through a central
unit dispatching the optimal policy computed by minimizing the overall social
cost. An approximate solution is obtained by learning the optimal policy of a
generic agent interacting with the statistical distribution of the states of
the other agents. We prove rigorously the convergence of exact and model-free
policy gradient methods in a mean-field linear-quadratic setting. We also
provide graphical evidence of the convergence based on implementations of our
algorithms.
