Quantitative convergence of finite population approximations for mean field control problems
Abstract
We study the approximation of mean field control problems by systems of interacting controlled particles, focusing on quantitative convergence rates for the associated value functions. We first establish non-asymptotic convergence bounds in discrete time, allowing for common noise and interactions through both states and controls. We then extend these results to path-dependent models, where the convergence rates reflect the increasing dimension of the discretized path space. Our approach relies on dynamic programming arguments combined with Wasserstein estimates for empirical measures of independent, not necessarily identically distributed random variables. In continuous time, we combine these estimates with uniform time-discretization bounds to obtain an explicit logarithmic convergence rate for path-dependent McKean–Vlasov control problems. Numerical experiments illustrate our theoretical results and highlight the influence of path dependence on convergence rates.
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About the speaker
Mehdi Talbi is an Assistant Professor (Maître de conférences) at Université Paris Cité and a member of the mathematical finance group at the Laboratoire de Probabilités, Statistiques et Modélisation (LPSM). His research lies at the intersection of stochastic control, mean field games, contract theory, and numerical probability, with a particular interest in optimal stopping and stochastic systems involving large populations. Before joining Université Paris Cité, he obtained his PhD in Applied Mathematics from Institut Polytechnique de Paris, and was a postdoctoral researcher at ETH Zürich.