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arXiv · 2203.14554

An algebraic convergence rate for the optimal control of McKean-Vlasov dynamics

Pierre Cardaliaguet·Samuel Daudin·Joe Jackson·Panagiotis Souganidis
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Abstract

We establish an algebraic rate of convergence in the large number of players limit 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 semi-concavity estimates for the N-particle value functions as well as a certain concentration inequality.

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Pierre Cardaliaguet, Samuel Daudin, Joe Jackson, Panagiotis Souganidis. 2022-03-28. An algebraic convergence rate for the optimal control of McKean-Vlasov dynamics. https://arxiv.org/abs/2203.14554

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