IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v21y2024i1d10.1007_s10287-023-00485-9.html
   My bibliography  Save this article

Decentralized saddle-point problems with different constants of strong convexity and strong concavity

Author

Listed:
  • Dmitry Metelev

    (Moscow Institute of Physics and Technology)

  • Alexander Rogozin

    (Moscow Institute of Physics and Technology
    HSE University)

  • Alexander Gasnikov

    (Moscow Institute of Physics and Technology
    HSE University
    ISP RAS Research Center for Trusted Artificial Intelligence)

  • Dmitry Kovalev

    (King Abdullah University of Science and Technology)

Abstract

Large-scale saddle-point problems arise in such machine learning tasks as GANs and linear models with affine constraints. In this paper, we study distributed saddle-point problems with strongly-convex–strongly-concave smooth objectives that have different strong convexity and strong concavity parameters of composite terms, which correspond to min and max variables, and bilinear saddle-point part. We consider two types of first-order oracles: deterministic (returns gradient) and stochastic (returns unbiased stochastic gradient). Our method works in both cases and takes several consensus steps between oracle calls.

Suggested Citation

  • Dmitry Metelev & Alexander Rogozin & Alexander Gasnikov & Dmitry Kovalev, 2024. "Decentralized saddle-point problems with different constants of strong convexity and strong concavity," Computational Management Science, Springer, vol. 21(1), pages 1-41, June.
    • Handle: RePEc:spr:comgts:v:21:y:2024:i:1:d:10.1007_s10287-023-00485-9
    DOI: 10.1007/s10287-023-00485-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-023-00485-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10287-023-00485-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2011. "First-order methods of smooth convex optimization with inexact oracle," LIDAM Discussion Papers CORE 2011002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jueyou Li & Zhiyou Wu & Changzhi Wu & Qiang Long & Xiangyu Wang, 2016. "An Inexact Dual Fast Gradient-Projection Method for Separable Convex Optimization with Linear Coupled Constraints," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 153-171, January.
    2. Masaru Ito, 2016. "New results on subgradient methods for strongly convex optimization problems with a unified analysis," Computational Optimization and Applications, Springer, vol. 65(1), pages 127-172, September.
    3. TAYLOR, Adrien B. & HENDRICKX, Julien M. & François GLINEUR, 2016. "Exact worst-case performance of first-order methods for composite convex optimization," LIDAM Discussion Papers CORE 2016052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Xuexue Zhang & Sanyang Liu & Nannan Zhao, 2023. "An Extended Gradient Method for Smooth and Strongly Convex Functions," Mathematics, MDPI, vol. 11(23), pages 1-14, November.
    5. Masoud Ahookhosh, 2019. "Accelerated first-order methods for large-scale convex optimization: nearly optimal complexity under strong convexity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 319-353, June.
    6. Julian Rasch & Antonin Chambolle, 2020. "Inexact first-order primal–dual algorithms," Computational Optimization and Applications, Springer, vol. 76(2), pages 381-430, June.
    7. Liam Madden & Stephen Becker & Emiliano Dall’Anese, 2021. "Bounds for the Tracking Error of First-Order Online Optimization Methods," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 437-457, May.
    8. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2013. "First-order methods with inexact oracle: the strongly convex case," LIDAM Discussion Papers CORE 2013016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. NESTEROV, Yurii, 2013. "Universal gradient methods for convex optimization problems," LIDAM Discussion Papers CORE 2013026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Le Thi Khanh Hien & Cuong V. Nguyen & Huan Xu & Canyi Lu & Jiashi Feng, 2019. "Accelerated Randomized Mirror Descent Algorithms for Composite Non-strongly Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 541-566, May.
    11. DEVOLDER, Olivier, 2011. "Stochastic first order methods in smooth convex optimization," LIDAM Discussion Papers CORE 2011070, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Kimon Fountoulakis & Rachael Tappenden, 2018. "A flexible coordinate descent method," Computational Optimization and Applications, Springer, vol. 70(2), pages 351-394, June.
    13. Ya-Feng Liu & Xin Liu & Shiqian Ma, 2019. "On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 632-650, May.
    14. Fedor Stonyakin & Alexander Gasnikov & Pavel Dvurechensky & Alexander Titov & Mohammad Alkousa, 2022. "Generalized Mirror Prox Algorithm for Monotone Variational Inequalities: Universality and Inexact Oracle," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 988-1013, September.
    15. Fedor Stonyakin & Ilya Kuruzov & Boris Polyak, 2023. "Stopping Rules for Gradient Methods for Non-convex Problems with Additive Noise in Gradient," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 531-551, August.
    16. Adrien B. Taylor & Julien M. Hendrickx & François Glineur, 2018. "Exact Worst-Case Convergence Rates of the Proximal Gradient Method for Composite Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 455-476, August.
    17. Stefan Richter & Colin Jones & Manfred Morari, 2013. "Certification aspects of the fast gradient method for solving the dual of parametric convex programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 305-321, June.
    18. Chengjing Wang & Peipei Tang, 2017. "A primal majorized semismooth Newton-CG augmented Lagrangian method for large-scale linearly constrained convex programming," Computational Optimization and Applications, Springer, vol. 68(3), pages 503-532, December.
    19. J. O. Royset & E. Y. Pee, 2012. "Rate of Convergence Analysis of Discretization and Smoothing Algorithms for Semiinfinite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 855-882, December.
    20. Ion Necoara, 2021. "General Convergence Analysis of Stochastic First-Order Methods for Composite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 66-95, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:comgts:v:21:y:2024:i:1:d:10.1007_s10287-023-00485-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.