Entropic Optimal Transport: Geometry and Large Deviations
| Autor: | Espen Bernton, Promit Ghosal, Marcel Nutz |
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| Rok vydání: | 2021 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2102.04397 |
| Popis: | We study the convergence of entropically regularized optimal transport to optimal transport. The main result is concerned with the convergence of the associated optimizers and takes the form of a large deviations principle quantifying the local exponential convergence rate as the regularization parameter vanishes. The exact rate function is determined in a general setting and linked to the Kantorovich potential of optimal transport. Our arguments are based on the geometry of the optimizers and inspired by the use of $c$-cyclical monotonicity in classical transport theory. The results can also be phrased in terms of Schr\"odinger bridges. Comment: Forthcoming in 'Duke Mathematical Journal' |
| Databáze: | OpenAIRE |
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