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 $\varepsilon$-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.
Cite
Text
Delalande. "Nearly Tight Convergence Bounds for Semi-Discrete Entropic Optimal Transport." Artificial Intelligence and Statistics, 2022.Markdown
[Delalande. "Nearly Tight Convergence Bounds for Semi-Discrete Entropic Optimal Transport." Artificial Intelligence and Statistics, 2022.](https://mlanthology.org/aistats/2022/delalande2022aistats-nearly/)BibTeX
@inproceedings{delalande2022aistats-nearly,
title = {{Nearly Tight Convergence Bounds for Semi-Discrete Entropic Optimal Transport}},
author = {Delalande, Alex},
booktitle = {Artificial Intelligence and Statistics},
year = {2022},
pages = {1619-1642},
volume = {151},
url = {https://mlanthology.org/aistats/2022/delalande2022aistats-nearly/}
}