Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport

Abstract : This article describes a method 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). The idea is to overrelax the Bregman projection operators, allowing for faster convergence. In practice this corresponds to elevating the diagonal scaling factors to a given power, at each step of the algorithm. We propose a simple method for establishing global convergence by ensuring the decrease of a Lyapunov function at each step. An adaptive choice of overrelaxation parameter based on the Lyapunov function is constructed. We also suggest a heuristic to choose a suitable asymptotic overrelaxation parameter, based on a local convergence analysis. Our numerical experiments show a gain in convergence speed by an order of magnitude in certain regimes.
Type de document :
Pré-publication, Document de travail
NIPS'17 Workshop on Optimal Transport & Machine Learning. 2017
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https://hal.archives-ouvertes.fr/hal-01629985
Contributeur : Nicolas Papadakis <>
Soumis le : mardi 7 novembre 2017 - 09:38:47
Dernière modification le : mercredi 8 novembre 2017 - 01:16:18

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  • HAL Id : hal-01629985, version 1
  • ARXIV : 1711.01851

Citation

Alexis Thibault, Lenaic Chizat, Charles Dossal, Nicolas Papadakis. Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport. NIPS'17 Workshop on Optimal Transport & Machine Learning. 2017. 〈hal-01629985〉

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