AN ALGEBRAIC CONVERGENCE RATE FOR THE OPTIMAL CONTROL OF MCKEAN-VLASOV DYNAMICS

Pierre Cardaliaguet (1) , Samuel Daudin (1) , Joe Jackson (2) , Panagiotis Souganidis (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Department of Mathematics [Austin]
3 Department of Mathematics [Chicago]

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.

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet, Samuel Daudin, Joe Jackson, Panagiotis Souganidis. AN ALGEBRAIC CONVERGENCE RATE FOR THE OPTIMAL CONTROL OF MCKEAN-VLASOV DYNAMICS. SIAM Journal on Control and Optimization, 2023, 61 (6), pp.3341-3369. ⟨10.1137/22M1486789⟩. ⟨hal-03618944v2⟩