Speaker: Daniel Lacker
Title: Non-asymptotic perspectives on mean field approximations and stochastic control
Abstract: The main focus of this talk is the analysis of high-dimensional stochastic control problems in which many agents cooperate to minimize a convex cost function. Our main results are sharp yet general bounds on the optimality gap between the full-information problem, in which each agent observes the states of all other agents, versus the distributed problem, in which each agent observes only its own state. Being decidedly non-asymptotic, our approach avoids structural constraints like exchangeability which are normally required in order to identify limiting objects but which rule out network-based models. A protagonist in our approach, dubbed the “independent projection,” is a general method for approximating a given high-dimensional diffusion process by one in which the coordinates are independent. This approximation is canonical in certain senses and enjoys interesting connections with the variational inference from Bayesian statistics and the theory of gradient flows in Wasserstein space.