An overview of entropy-regularized optimal transport and Schrödinger bridges

The theory of Monge-Kantorovich optimal transport has recently become popular in various applications in statistics and data science. Part of this popularity is due to a regularized version of the problem with the entropy serving as a penalty function. The addition of entropy as a regularizer provides smoothness, robustness, computational efficiency, and much more. This presentation will provide an overview of this rapidly evolving research area including some recently discovered connections with score function estimation and transformers.