Two-Sided Bounds for Entropic Optimal Transport via a Rate-Distortion Integral

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1. Verfasser: Liu, Jingbo
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Veröffentlicht: 2026
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author Liu, Jingbo
author_facet Liu, Jingbo
contents We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the rate-distortion function, up to universal multiplicative constants. The proof is based on a lifting technique, which constructs a Gaussian process indexed by a random subset of the type class of the probability distribution involved in the information-theoretic inequality, and then applying a form of the majorizing measure theorem.
format Preprint
id arxiv_https___arxiv_org_abs_2604_14061
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Two-Sided Bounds for Entropic Optimal Transport via a Rate-Distortion Integral
Liu, Jingbo
Information Theory
Probability
Machine Learning
We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the rate-distortion function, up to universal multiplicative constants. The proof is based on a lifting technique, which constructs a Gaussian process indexed by a random subset of the type class of the probability distribution involved in the information-theoretic inequality, and then applying a form of the majorizing measure theorem.
title Two-Sided Bounds for Entropic Optimal Transport via a Rate-Distortion Integral
topic Information Theory
Probability
Machine Learning
url https://arxiv.org/abs/2604.14061