THIBAULT, Alexis; CHIZAT, Lenaic; DOSSAL, Charles; PAPADAKIS, Nicolas

Métadonnées

Licence d’utilisation du document

CHIZAT, Lenaic
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

DOSSAL, Charles
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Institut de Mathématiques de Toulouse UMR5219 [IMT]

Langue

Communication dans un congrès

Ce document a été publié dans

NIPS Workshop on Optimal Transport & Machine Learning (OTML'17), 2017-12-09, Long Beach.

Résumé en anglais

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.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192806

Project ANR

Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251