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    Decentralized Computation of Wasserstein Barycenter over Time-Varying Networks

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    2205.15669.pdf
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    Description:
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    Type
    Preprint
    Authors
    Yufereva, Olga
    Persiianov, Michael
    Dvurechensky, Pavel
    Gasnikov, Alexander
    Kovalev, Dmitry cc
    KAUST Department
    Computer Science
    Computer Science Program
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    King Abdullah University of Science and Technology
    Date
    2022-05-31
    Permanent link to this record
    http://hdl.handle.net/10754/678603
    
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    Abstract
    Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are motivated by examples when only a subset of sensors can make an observation at each time step, and yet, the goal is to average signals (e.g., satellite pictures of some area) by approximating their barycenter. We prove non-asymptotic accelerated in the sense of Nesterov convergence rates and explicitly characterize their dependence on the parameters of the network and its dynamics. Our approach is based on our novel distributed non-smooth optimization method on time-varying networks, which may be of separate interest. In the experiments, we demonstrate the efficiency of the proposed algorithm.
    Sponsors
    The work of A. Gasnikov in the first part of the paper was funded by Russian Science Foundation (project 18-71-10108). The work of O. Yufereva in the second part of the paper was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2022-874).
    Publisher
    arXiv
    arXiv
    2205.15669
    Additional Links
    https://arxiv.org/pdf/2205.15669.pdf
    Collections
    Preprints; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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