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Title: Wasserstein gradient flows of entropic optimal transport Authors:  Lenaic Chizat - EPFL (Switzerland) [presenting]
Abstract: Entropic Optimal Transport (EOT) is a modification of the Optimal Transport problem that is statistically and computationally more tractable, and that is a building block of several useful tools in machine learning (Sinkhorn divergence, barycenters of measures, trajectory inference, etc). We study the well-posedness, and the long-time behavior of Wasserstein gradient flows of functionals involving EOT on a compact domain. The well-posedness relies on a stable result for the solutions of the dual EOT problem, and the long-time behavior follows from a nonlinear generalization of the convergence of overdamped Langevin dynamics via log-Sobolev inequalities. Finally, we will discuss applications to the grid-free computation of regularized Wasserstein barycenters and the problem of trajectory inference.