Global Regularity Estimates for Optimal Transport via Entropic Regularisation

TL;DR

This paper introduces a novel approach to establish global regularity estimates for quadratic optimal transport problems by leveraging entropic regularisation and the Prekopa-Leindler inequality, advancing theoretical understanding.

Contribution

It provides a new method combining entropic regularisation with classical inequalities to prove regularity in optimal transport, which was previously unresolved.

Findings

Established global regularity estimates for quadratic optimal transport

Demonstrated the effectiveness of entropic regularisation in theoretical analysis

Connected entropic regularisation with classical inequalities for optimal transport

Abstract

We develop a general approach to prove global regularity estimates for quadratic optimal transport using the entropic regularisation of the problem and the Prekopa-Leindler inequality.