Speaker
Giovanni Conforti
Description
Entropy minimization problems under marginal constraints play a central role in machine learning, data science, and computational optimal transport. Prominent examples include entropic optimal transport and the (regularized) Wasserstein barycenter problem. This talk presents general principles for establishing quantitative stability of entropic projections. In particular, I will show how semiconcavity of the dual variables yields a form of entropic stability for the optimal plans, which in turn implies exponential convergence of the Sinkhorn algorithm with sharp rates. Time permitting, I will also discuss how to prove semiconcavity of the optimal potentials under geometric assumptions on the marginals.