Convergence Rates for Regularized Optimal Transport via Quantization

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Stephan Eckstein, Marcel Nutz

Published: 2024, Last Modified: 25 Jan 2026Math. Oper. Res. 2024EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. Sharp rates for general divergences including relative entropy or Lp 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. Funding: This work was supported by the Alfred P. Sloan Foundation [Grant FG-2016-6282] and the Division of Mathematical Sciences [Grants DMS-1812661 and DMS-2106056].