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Convergence Rates for Regularized Optimal Transport via Quantization (2208.14391v3)

Published 30 Aug 2022 in math.OC, math.PR, and stat.ML

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 multi-marginal problems are obtained. A novel methodology using quantization and martingale couplings is suitable for non-compact marginals and achieves, in particular, the sharp leading-order term of entropically regularized 2-Wasserstein distance for all marginals with finite $(2+\delta)$-moment.

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