Wasserstein Gradient flows of Entropic Optimal Transport
speaker: Lénaïc Chizat (EPFL)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). In this talk, 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 stability 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. If time permit, we will discuss applications to the grid-free computation of regularized Wasserstein barycenters and to the problem of trajectory inference.
timetable:
Tue 25 Oct, 11:00 - 11:45, Aula Magna Bruno Pontecorvo
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