On the linear convergence of the multi-marginal Sinkhorn algorithm

Carlier, Guillaume

Carlier, Guillaume (2021), On the linear convergence of the multi-marginal Sinkhorn algorithm. https://basepub.dauphine.psl.eu/handle/123456789/22372

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Type

Document de travail / Working paper

External document link

https://hal.archives-ouvertes.fr/hal-03176512

Date

2021

Series title

Cahier de recherche du CEREMADE

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Author(s)

Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Abstract (EN)

The aim of this short note is to give an elementary proof of linear convergence of the Sinkhorn algorithm for the entropic regularization of multi-marginal optimal transport. The proof simply relies on: i) the fact that Sinkhorn iterates are bounded, ii) strong convexity of the exponential on bounded intervals and iii) the convergence analysis of the coordinate descent (Gauss-Seidel) method of Beck and Tetruashvili [1].

Subjects / Keywords

Block coordinate descent; Linear convergence; Sinkhorn algorithm; Multi-marginal entropic optimal transport