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

• URL: http://arxiv.org/abs/2604.14061v1
• Date: Wed, 15 Apr 2026 16:37:00 GMT
• Title: Two-Sided Bounds for Entropic Optimal Transport via a Rate-Distortion Integral
• Abstract summary: We show that the maximum expected inner product between a random vector and the standard normal vector is equivalent to a truncated integral involving the rate-distortion function.<n>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.
• Score: 17.319855487817257
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: 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.

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