Giovanni Conforti - Regularity of entropic potentials, stability of entropic optimal transport... скачать в хорошем качестве

Giovanni Conforti - Regularity of entropic potentials, stability of entropic optimal transport...

This lecture was part of the Workshop on "Probabilistic Mass Transport - from Schrödinger to Stochastic Analysis" held at the ESI February 9 - 13, 2026. For most optimization problems, regularity of optimal solutions implies stability of optimizers with respect to perturbations in the problem’s parameters or constraints. In turn, this stability can be leveraged to establish theoretical convergence guarantees for numerical schemes. The aim of this talk is to explore this chain of implications in the context of the entropic optimal transport problem. More precisely, I will first discuss a probabilistic approach to the problem of establishing monotonicity estimates for the gradients of Schrödinger potentials. Next, I will explain how weak semiconcavity of the potentials implies stability of optimal plans with respect to the marginal inputs, and how this stability is a key ingredient in proving the exponential convergence of Sinkhorn’s algorithm.