An improved central limit theorem and fast convergence rates for entropic transportation costs
This work addresses statistical inference challenges in optimal transport for researchers, offering incremental improvements with new theoretical guarantees.
The paper proves a central limit theorem for entropic transportation costs between subgaussian measures, enabling asymptotically valid inference for non-discrete measures, and provides faster convergence rates for empirical measures in compactly supported cases.
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.