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

TL;DR

This paper establishes a central limit theorem for entropic transportation costs between subgaussian measures, enabling valid inference beyond discrete cases, and introduces faster convergence rates for empirical measures.

Contribution

It provides the first CLT for entropic OT between non-discrete measures and improves convergence rates for empirical entropic transportation costs.

Findings

CLT for entropic transportation costs between subgaussian measures

Faster convergence rates for empirical entropic transportation costs

Extension of inference validity to non-discrete measures

Abstract

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.