Sinkhorn algorithm is an iterative fitting procedure that allows to quickly compute the unique solution of the Entropic Optimal Transport problem, i.e. the entropic regularization of the Kantorovich-OT problem. Despite its wide use in applications, the study of its convergence rate is still a very active area of research. Particularly in the unbounded setting, where it has not been proven its exponential convergence, so far. In this talk, after a small introduction on the quadratic EOT problem and its equivalence stochastic formulation (namely the Schrödinger problem), we are going to prove that Sinkhorn algorithm converges exponentially fast for a wide class of (unbounded) marginals. More precisely we are going to prove convergence of the iterated plans in terms of relative entropies, and convergence of the iterated potentials and of their gradients (pointwise and in L^1). Our approach relies on a stochastic interpretation of Sinkhorn iterations and on coupling techniques.
Based on a joint work with G. Conforti and A. Durmus
Elise Bonhomme
