A Gradient Descent Perspective on Sinkhorn

We present a new perspective on the popular Sinkhorn algorithm, showing that it can be seen as a Bregman gradient descent (mirror descent) of a relative entropy (Kullback–Leibler divergence). This viewpoint implies a new sublinear convergence rate with a robust constant.

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Bibliographische Detailangaben
Veröffentlicht in:	Applied mathematics & optimization 2021-10, Vol.84 (2), p.1843-1855
1. Verfasser:	Léger, Flavien
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Calculus of Variations and Optimal Control Optimization Control Entropy Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical and Computational Physics Simulation Systems Theory Theoretical
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Beschreibung
Zusammenfassung:	We present a new perspective on the popular Sinkhorn algorithm, showing that it can be seen as a Bregman gradient descent (mirror descent) of a relative entropy (Kullback–Leibler divergence). This viewpoint implies a new sublinear convergence rate with a robust constant.
ISSN:	0095-4616 1432-0606
DOI:	10.1007/s00245-020-09697-w