Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport

arXiv2110.12678MaRDI QIDQ6381174

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Publication date: 25 October 2021

Abstract: We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn potentials) w.r.t. the regularization parameter, for which we ensure a better than Lipschitz dependence. Such facts may be a first step towards a mathematical justification of annealing or $varepsilon$-scaling heuristics for the numerical resolution of regularized semi-discrete optimal transport. Our results also entail a non-asymptotic and tight expansion of the difference between the entropic and the unregularized costs.

Has companion code repository: https://github.com/alex-delalande/potentials-entropic-sd-ot

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