High-accuracy Sampling From Constrained Spaces: An Optimization Perspective

This talk views the problem of sampling from distributions supported on a convex body through the lens of classical non-Euclidean optimization methods namely mirror methods and natural gradient methods. These respectively form the basis of two new algorithms for constrained sampling — the Metropolis-Adjusted Mirror-Langevin Algorithm and the Metropolis-Adjusted Preconditioned Langevin Algorithm, which I will present in this talk. This talk will focus on the mixing time guarantees of these algorithms — an essential theoretical property for MCMC methods — under natural conditions over the target distribution and the geometry of the domain.