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Algorithms for Euclidean-Regularised Optimal Transport

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Optimization and Applications (OPTIMA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14395))

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Abstract

This paper addresses the Optimal Transport problem, which is regularized by the square of Euclidean \(\ell _2\)-norm. It offers theoretical guarantees regarding the iteration complexities of the Sinkhorn–Knopp algorithm, Accelerated Gradient Descent, Accelerated Alternating Minimisation, and Coordinate Linear Variance Reduction algorithms. Furthermore, the paper compares the practical efficiency of these methods and their counterparts when applied to the entropy-regularized Optimal Transport problem. This comparison is conducted through numerical experiments carried out on the MNIST dataset.

The research was supported by Russian Science Foundation (project No. 23-11-00229), https://rscf.ru/en/project/23-11-00229/, and by the grant of support for leading scientific schools NSh775.2022.1.1.

D. A. Pasechnyuk and M. Persiianov—Equal contribution.

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Notes

  1. 1.

    Repository is available at https://github.com/MuXauJl11110/Euclidean-Regularised-Optimal-Transport.

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Author information

Authors and Affiliations

  1. Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE

    Dmitry A. Pasechnyuk

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    Dmitry A. Pasechnyuk, Michael Persiianov & Alexander Gasnikov

  3. ISP RAS Research Center for Trusted Artificial Intelligence, Moscow, Russia

    Dmitry A. Pasechnyuk

  4. Institute for Information Transmission Problems RAS, Moscow, Russia

    Dmitry A. Pasechnyuk, Michael Persiianov & Alexander Gasnikov

  5. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Pavel Dvurechensky

  6. Caucasus Mathematic Center of Adygh State University, Maikop, Russia

    Alexander Gasnikov

Authors
  1. Dmitry A. Pasechnyuk
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  2. Michael Persiianov
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  3. Pavel Dvurechensky
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  4. Alexander Gasnikov
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Corresponding author

Correspondence to Dmitry A. Pasechnyuk .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Pasechnyuk, D.A., Persiianov, M., Dvurechensky, P., Gasnikov, A. (2023). Algorithms for Euclidean-Regularised Optimal Transport. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2023. Lecture Notes in Computer Science, vol 14395. Springer, Cham. https://doi.org/10.1007/978-3-031-47859-8_7

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  • DOI: https://doi.org/10.1007/978-3-031-47859-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-47858-1

  • Online ISBN: 978-3-031-47859-8

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