Convergence Rates for Regularized Optimal Transport via Quantization

Stephan Eckstein () and Marcel Nutz ()
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Stephan Eckstein: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
Marcel Nutz: Departments of Statistics and Mathematics, Columbia University, New York, New York 10027

Mathematics of Operations Research, 2024, vol. 49, issue 2, 1223-1240

Abstract: We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. Sharp rates for general divergences including relative entropy or L p regularization, general transport costs, and multimarginal problems are obtained. A novel methodology using quantization and martingale couplings is suitable for noncompact marginals and achieves, in particular, the sharp leading-order term of entropically regularized 2-Wasserstein distance for marginals with a finite ( 2 + δ ) -moment.

Keywords: Primary: 90C25; 49N05; entropic optimal transport; f -divergence; regularization; quantization (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:2:p:1223-1240

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