The JKO scheme based on Sinkhorn divergences

par Aymeric Baradat

mercredi 4 nov. 2026, 10:00 → 12:00 Europe/Paris

112 TBC (Braconnier )

When computing numerically solutions of Wasserstein gradient flows through the JKO scheme, it can be useful to use an entropic version of the classical optimal transport problem in order to fasten the computations. However, a drawback of this method is that the entropic cost between two measures a and b is not minimal for a = b. Therefore, this implies an additional dynamic, and for instance, the sequence produced by the scheme does not converge towards the minimizer of the energy functional of study. A way to solve this issue is to use the Sinkhorn divergence, obtained by removing to the entropic optimal transport cost S(a,b) the quantity (S(a,a) + S(b,b))/2, so that the resulting cost cancels when a = b. In this talk, I will show that this version of the entropic JKO scheme in the case of a linear energy functional recovers the convergence towards minimizers, I will describe formally the limiting curve obtained when the timestep goes to 0, and I will prove convergence in the case of a finite base space. The talk is based on a paper by Hardion and Lavenant.