An algebraic convergence rate for the optimal control of McKean-Vlasov dynamics
Optimization and Control
2023-01-09 v2
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.
Keywords
Cite
@article{arxiv.2203.14554,
title = {An algebraic convergence rate for the optimal control of McKean-Vlasov dynamics},
author = {Pierre Cardaliaguet and Samuel Daudin and Joe Jackson and Panagiotis Souganidis},
journal= {arXiv preprint arXiv:2203.14554},
year = {2023}
}