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Preprints, Working Papers, ... Year : 2024

Displacement smoothness of entropic optimal transport

Abstract

The function that maps a family of probability measures to the solution of the dual entropic optimal transport problem is known as the Schrödinger map. We prove that when the cost function is $C^{k+1}$ with k in N* then this map is Lipschitz continuous from the $L^2$-Wasserstein space to the space of $C^k$ functions. Our result holds on compact domains and covers the multi-marginal case. As applications, we prove displacement smoothness of the entropic optimal transport cost and the well-posedness of certain Wasserstein gradient flows involving this functional, including the Sinkhorn divergence and a multi-species system.
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Dates and versions

hal-03793562 , version 1 (01-10-2022)
hal-03793562 , version 2 (01-03-2024)

Identifiers

  • HAL Id : hal-03793562 , version 2

Cite

Guillaume Carlier, Lénaïc Chizat, Maxime Laborde. Displacement smoothness of entropic optimal transport. 2024. ⟨hal-03793562v2⟩
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