Abstract: We present a finite-dimensional global numerical approximation for a class of extended mean field control problems. Our algorithm learns the value function on the whole Wasserstein domain, as opposed to a fixed initial condition. We leverage the approximation of the mean field problem by a finite-player cooperative optimisation problem, due to the propagation of chaos, together with the usage of finite-dimensional solvers. This avoids the need to directly approximate functions on an infinite-dimensional domain, and allows for more efficient memory usage and faster computation. 

Joint work with Athena Picarelli and Marco Scaratti (University of Verona).

Bios: Jonathan Tam is currently Department Lecturer in the Mathematical and Computational Finance group at the University of Oxford. His research is focused around decision making under uncertainty, through the lens of stochastic control and mean-field games, with applications in mathematical finance and computational methods.