On the sample complexity of entropic optimal transport

TL;DR

This paper investigates the sample complexity of entropic optimal transport in high dimensions, providing dimension-free, parametric rates for estimation and proposing a transfer learning model with theoretical guarantees.

Contribution

It establishes dimension-free, parametric convergence rates for entropic optimal transport estimators and introduces a practical transfer learning framework based on these methods.

Findings

Achieved dimension-free, parametric rates for entropic regression functions.

Proposed a transfer learning model with provable convergence guarantees.

Demonstrated practical applicability in nonparametric regression and classification.

Abstract

We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by establishing dimension-free, parametric rates for estimating various quantities of interest, including the entropic regression function which is a natural analog to the optimal transport map. As an application, we propose a practical model for transfer learning based on entropic optimal transport and establish parametric rates of convergence for nonparametric regression and classification.