FRE Special Seminar: Joe Jackson

This event is free, but registration is required.

Title

Mean Field Control with Absorption

Abstract

In a typical mean field control problem, a central planner controls a large number of particles with the aim of minimizing a symmetric cost functional. As the number N of particles tends to infinity, the N-particle optimization problem converges in an appropriate sense to a control problem of McKean-Vlasov type, whose value function satisfies an infinite-dimensional Hamilton-Jacobi-Bellman (HJB) equation set on a space of probability measures. In this talk, I will introduce a version of mean field control in which each particle is absorbed if it reaches the boundary of a smooth domain. Because mass can decrease over time due to absorption, the limiting HJB equation is set on a space of sub-probability measures and features a non-standard boundary condition. We develop a viscosity solution theory for this novel HJB equation, and then use the uniqueness of viscosity solutions to establish the convergence of the N-particle model to its mean field limit. This is joint work with Pierre Cardaliaguet and Panagiotis E. Souganidis.

Bio

Joe is a Dickson Instructor and NSF Postdoctoral Research Fellow at the University of Chicago. He earned his PhD in mathematics in 2023 from the University of Texas at Austin. His research interests are in partial differential equations, stochastic analysis, mean field games and mean field control.