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Conference Papers Year : 2022

Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport

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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Dates and versions

hal-03396206 , version 1 (22-10-2021)
hal-03396206 , version 2 (29-11-2021)

Identifiers

  • HAL Id : hal-03396206 , version 2

Cite

Alex Delalande. Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport. AISTATS 2022 - 25th International Conference on Artificial Intelligence and Statistics, Mar 2022, Valencia / Virtual, Spain. pp.1619-1642. ⟨hal-03396206v2⟩
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