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Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport

hal.structure.identifierModélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes [MAKUTU]
dc.contributor.authorTHIBAULT, Alexis
hal.structure.identifierLaboratoire de Mathématiques d'Orsay [LMO]
dc.contributor.authorCHIZAT, Lénaïc
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
hal.structure.identifierInstitut National des Sciences Appliquées - Toulouse [INSA Toulouse]
dc.contributor.authorDOSSAL, Charles
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAPADAKIS, Nicolas
dc.date.accessioned2024-04-04T02:46:35Z
dc.date.available2024-04-04T02:46:35Z
dc.date.issued2021
dc.identifier.issn1999-4893
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191566
dc.description.abstractEnThis 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.
dc.description.sponsorshipGeneralized Optimal Transport Models for Image processing - ANR-16-CE33-0010
dc.language.isoen
dc.publisherMDPI
dc.title.enOverrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport
dc.typeArticle de revue
dc.identifier.doi10.3390/a14050143
dc.subject.halStatistiques [stat]/Machine Learning [stat.ML]
bordeaux.journalAlgorithms
bordeaux.volume14
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue5
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03212175
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03212175v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Algorithms&rft.date=2021&rft.volume=14&rft.issue=5&rft.eissn=1999-4893&rft.issn=1999-4893&rft.au=THIBAULT,%20Alexis&CHIZAT,%20L%C3%A9na%C3%AFc&DOSSAL,%20Charles&PAPADAKIS,%20Nicolas&rft.genre=article


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