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

2023; Society for Industrial and Applied Mathematics; Volume: 61; Issue: 6 Linguagem: Inglês

10.1137/22m1486789

1095-7138

Pierre Cardaliaguet, Samuel Daudin, Joe Jackson, Panagiotis E. Souganidis,

Hemodynamic Monitoring and Therapy

.We establish an algebraic rate of convergence of the value functions of \(N\)-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 \(N\) Lipschitz and semiconcavity estimates for the \(N\)-particle value functions as well as a certain concentration inequality.Keywordsmean field controlMcKean–Vlasov dynamicsconvergence rateMSC codes93E2060H30