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Seminar on Control Theory and Nonlinear Filtering
An optimization perspective on log-concave sampling
An optimization perspective on log-concave sampling
Organizer
Speaker
Time
Wednesday, March 20, 2024 3:00 PM - 3:30 PM
Venue
理科楼A-304
Abstract
The primary contribution of this thesis is to advance the theory of complexity for sampling from a continuous probability density over R^d. Some highlights are included: a new analysis of the proximal sampler, taking inspiration from the proximal point algorithm in optimization; an improved and sharp analysis of the Metropolis-adjusted Langevin algorithm, yielding new state-of-the-art guarantees for high-accuracy log-concave sampling; the first lower bounds for the complexity of log-concave sampling; an analysis of mirror Langevin Monte Carlo for constrained sampling; and the development of a theory of approximate first-order stationarity in non-log-concave sampling.