The entropic optimal transport problem is a regularised version of the classical optimal transport problem which consists in minimising relative entropy against a reference distribution among all couplings of two given marginals. In this talk, we study stability of optimisers and exponential convergence of Sinkhorn’s algorithm, that is widely used to solve EOT in practice.  In the first part of the talk, we will illustrate how semiconcavity of dual optimal variables, known as entropic potentials, plays a key role in understanding both problems. In the second part of the talk we discuss how to establish semiconcavity bounds in examples of interest such as  log-concave marginals or marginals with bounded support.

Joint work with A. Chiarini, G.Greco and L. Tamanini