Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport

• URL: http://arxiv.org/abs/2110.12678v1
• Date: Mon, 25 Oct 2021 06:52:45 GMT
• Title: Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport
• Authors: Alex Delalande (LMO, DATASHAPE)
• Abstract summary: We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. Our results also entail a non-asymptotic and tight expansion of the difference between the entropic and the unregularized costs.
• Score: 0.483420384410068
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\eps$-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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