Un Mokameeting aura lieu le mercredi 8 février 2023, à 14h, dans la salle A415. Nous aurons le plaisir d’écouter Alex Delalande (LMO & Inria)
Titre : Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport
Résumé : In this talk, I will present some nearly tight and non-asymptotic convergence bounds for the solutions of entropic semi-discrete optimal transport problems with a quadratic ground cost. These bounds quantify the stability of the dual solutions of the regularized transport problem (sometimes called Schrödinger or Sinkhorn potentials) with respect to the regularization parameter, for which a better than Lipschitz dependence is showcased. Such facts may be a first step towards a mathematical justification of annealing or ε-scaling heuristics for the numerical resolution of regularized semi-discrete optimal transport. These bounds also entail a non-asymptotic and tight expansion of the difference between the entropic and the unregularized optimal transport costs in the semi-discrete setting.
I will present the main arguments used to prove these bounds, which rely in particular on an estimation of the strong-convexity of the dual problem that holds beyond the semi-discrete and entropic setting.
