An Algebraic Convergence Rate for the Optimal Control of McKean–Vlasov Dynamics

Abstract

Abstract. We establish an algebraic rate of convergence of the value functions of [Formula: see text]-particle stochastic control problems towards the value function of the corresponding McKean–Vlasov problem, also known as mean field control. The rate is obtained in the presence of both idiosyncratic and common noises and in a setting where the value function for the McKean–Vlasov problem need not be smooth. Our approach relies crucially on uniform in [Formula: see text] Lipschitz and semiconcavity estimates for the [Formula: see text]-particle value functions as well as a certain concentration inequality.

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