Paper ID: 2204.09105

An improved central limit theorem and fast convergence rates for entropic transportation costs

Eustasio del Barrio, Alberto Gonzalez-Sanz, Jean-Michel Loubes, Jonathan Niles-Weed

We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal transport between measures which are not necessarily discrete. In the compactly supported case, we complement these results with new, faster, convergence rates for the expected entropic transportation cost between empirical measures. Our proof is based on strengthening convergence results for dual solutions to the entropic optimal transport problem.

Submitted: Apr 19, 2022