Convergence Rates for Regularized Optimal Transport via Quantization

08/30/2022

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by   Stephan Eckstein, et al.

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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+δ)-moment.