An optimization perspective on log-concave sampling and beyond

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 include: 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. We further illustrate the main tools in this work—diffusions and Wasserstein gradient flows—through applications to functional inequalities, the entropic barrier, Wasserstein barycenters, variational inference, and diffusion models.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2023

Author dc:creator

• Chewi, Sinho

Advisor dc:contributor.advisor

• Rigollet, Philippe

Statement dc:rights

• Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
• Copyright retained by author(s)

Licence dc:rights.uri

• https://creativecommons.org/licenses/by-sa/4.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/151333

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/151333