Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport

Alex Delalande

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arXiv · 2110.12678

Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport

Alex Delalande

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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.

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Alex Delalande. 2021-10-25. Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport. https://arxiv.org/abs/2110.12678

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