On the sample complexity of entropic optimal transport
Philippe Rigollet, Austin J. Stromme
The Annals of Statistics · 2025 · Volume 53 · Issue 1
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.
Keywords
62G05, entropic regularization, Optimal transport, Schrödinger bridge, statistical rates
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