$C^{1,\alpha}$-regularity for Schr\"odinger potentials of Shannon-entropy regularized Optimal Transport

TL;DR

This paper proves the stability of $C^{1,eta}$ regularity for Schr"odinger potentials in entropy-regularized optimal transport, assuming bounded convex marginals with bounded densities.

Contribution

It establishes the stability of $C^{1,eta}$ regularity for Schr"odinger potentials under classical bounded convex support assumptions.

Findings

Stability of $C^{1,eta}$ regularity proven

Applicable to marginals with bounded densities

Supports regularity analysis in entropy-regularized optimal transport

Abstract

We provide the stability of $C^{1,\alpha}$ regularity of Schr\"odinger potentials of Boltzmann-Shannon entropy regularized Optimal Transport under the classical assumption of marginals supported on bounded convex sets and whose densities are bounded above and below.