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Title: Convergence rates for regularized optimal transport via quantization Authors:  Stephan Eckstein - ETH Zürich (Switzerland) [presenting]
Marcel Nutz - Columbia University (United States)
Abstract: A simple approach is showcased to obtain sharp convergence rates for the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. The approach is based on quantization, where we balance an increasingly large discrete approximation of the marginals against a decreasing regularization parameter. The methodology is flexible and applicable to different divergences, multi-marginal problems and a large class of cost functions. Among others, this yields the sharp leading-order term for entropically regularized 2-Wasserstein distance under just $(2+\delta)$-moment assumption on the marginals.