Entropic Regularization of Optimal Transport and Applications

The mathematics of optimal transport (OT) has grown to become a unifying theme in many scientific disciplines, from solving purely mathematical problems of analysis, geometry, and partial differential equations to developing revolutionary new methods in economics, statistics, machine learning and artificial intelligence. In the last decade, the impact of optimal transport in the study of geometry was highlighted by two Fields medals (Villani 2010, Figalli 2018). On the other hand, OT has established itself as a viable alternative to classical maximum likelihood based methods in statistics and data science. Other notable applications include generative adversarial network (GAN) in machine learning (Wasserstein GAN), new applications to stem cell biology, and economic applications such as generalizations of the Nobel prize winning Gale-Shapley algorithm, online auctions, and option pricing.