An overview of entropy-regularized optimal transport and Schrödinger bridges
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Abstract
The theory of Monge-Kantorovich optimal transport has become widely popular in various areas of statistics, data science, and generative AI. Part of this popularity is due to a regularized version of the problem with the entropy serving as a penalty function. It turns out that the entropy-regularized version of optimal transport is itself mathematically rich and a confluence of ideas from physics, large deviations, stochastic processes, geometry, and PDEs. This presentation will provide an overview and many aspects of rapidly evolving current research. No background in optimal transport or entropy-regularized optimal transport will be assumed.
Soumik Pal is a Professor and the Robert B. Warfield, Jr., Endowed Faculty Fellow in the Department of Mathematics at the University of Washington, Seattle. He also holds adjunct professorships at the Department of Applied Mathematics and the Department of Statistics. His research interests are in probabilistic and statistical aspects of Monge-Kantorovich optimal transport theory. His other interests include mean-filed interacting particle systems, random graphs, and mathematical finance.