Overrelaxed Sinkhorn–Knopp Algorithm for Regularized Optimal Transport

This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm). We first proposed to rely on regularized nonlinear accelera...

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Veröffentlicht in:Algorithms Jg. 14; H. 5; S. 143
Hauptverfasser: Thibault, Alexis, Chizat, Lénaïc, Dossal, Charles, Papadakis, Nicolas
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 2021
MDPI
Schriftenreihe:Optimal Transport: Algorithms and Applications
Schlagworte:
Acceleration
Algorithms
Convergence
Efficiency
Iterative methods
Liapunov functions
Linear programming
Machine Learning
Methods
optimal transport
overrelaxation
Parameters
Sinkhorn–Knopp algorithm
Statistics
ISSN:1999-4893, 1999-4893
Online-Zugang:Volltext
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Zusammenfassung:This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm). We first proposed to rely on regularized nonlinear acceleration schemes. In practice, such approaches lead to fast algorithms, but their global convergence is not ensured. Hence, we next proposed a new algorithm with convergence guarantees. The idea is to overrelax the Bregman projection operators, allowing for faster convergence. We proposed a simple method for establishing global convergence by ensuring the decrease of a Lyapunov function at each step. An adaptive choice of the overrelaxation parameter based on the Lyapunov function was constructed. We also suggested a heuristic to choose a suitable asymptotic overrelaxation parameter, based on a local convergence analysis. Our numerical experiments showed a gain in convergence speed by an order of magnitude in certain regimes.
Bibliographie:ObjectType-Article-1
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content type line 14
ISSN:1999-4893
1999-4893
DOI:10.3390/a14050143