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    Decentralized Distributed Optimization for Saddle Point Problems

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    Type
    Preprint
    Authors
    Rogozin, Alexander
    Beznosikov, Alexander
    Dvinskikh, Darina
    Kovalev, Dmitry cc
    Dvurechensky, Pavel
    Gasnikov, Alexander
    KAUST Department
    Computer Science
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2021-02-15
    Permanent link to this record
    http://hdl.handle.net/10754/667615
    
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    Abstract
    We consider distributed convex-concave saddle point problems over arbitrary connected undirected networks and propose a decentralized distributed algorithm for their solution. The local functions distributed across the nodes are assumed to have global and local groups of variables. For the proposed algorithm we prove non-asymptotic convergence rate estimates with explicit dependence on the network characteristics. To supplement the convergence rate analysis, we propose lower bounds for strongly-convex-strongly-concave and convex-concave saddle-point problems over arbitrary connected undirected networks. We illustrate the considered problem setting by a particular application to distributed calculation of non-regularized Wasserstein barycenters.
    Sponsors
    The work of A. Rogozin and A. Beznosikov was supported by RFBR, project number 19-31-51001. The research of A. Gasnikov was supported by the Ministry of Science and Higher Education of the Russian Federation (Goszadaniye) 075-00337-20-03, project no. 0714-2020-0005.
    Publisher
    arXiv
    arXiv
    2102.07758
    Additional Links
    https://arxiv.org/pdf/2102.07758.pdf
    Collections
    Preprints; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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