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arXiv · 2102.04397

Entropic Optimal Transport: Geometry and Large Deviations

Espen Bernton·Promit Ghosal·Marcel Nutz
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Abstract

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.

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Espen Bernton, Promit Ghosal, Marcel Nutz. 2021-02-08. Entropic Optimal Transport: Geometry and Large Deviations. https://arxiv.org/abs/2102.04397

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