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

Cardaliaguet, Pierre; Daudin, Samuel; Jackson, Joe; Souganidis, Panagiotis E. (2022), An algebraic convergence rate for the optimal control of Mckean-Vlasov dynamics. https://basepub.dauphine.psl.eu/handle/123456789/23113

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
28
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Author(s)
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Daudin, Samuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Jackson, Joe
Department of Mathematics [Austin]
Souganidis, Panagiotis E.
Department of Mathematics [Chicago]
Abstract (EN)
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.