This was part of Decision Making and Uncertainty

Entropic Selection in Optimal Transport

Marcel Nutz, Columbia University

Tuesday, February 6, 2024


The optimal transport problem can admit many solutions, for instance when the cost function is the Euclidean distance on R^d (Monge's problem). On the other hand, entropically regularized optimal transport (EOT) always has a unique optimizer. It is a longstanding open problem whether EOT selects some particular optimal transport coupling in the vanishing regularization limit, and what that coupling would look like. We provide a surprising answer for Monge's problem in dimension d > 1. (Joint work with Chenyang Zhong.)