The mathematics of log-concave sampling

This talk presents the mathematical underpinnings of the results discussed in the preceding talk. For the problems of obtaining a warm start for high-accuracy samplers, and for achieving partial acceleration via a numerical discretization of the underdamped Langevin diffusion, we introduce a new framework—called shifted composition—which enables coupling-based analyses in KL and Rényi divergences. For lower bounds, we give information-theoretic arguments based on geometric constructions.