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Decentralized convex optimization on time-varying networks with application to Wasserstein barycenters

Author

Listed:
  • Olga Yufereva

    (N. N. Krasovskii Institute of Mathematics and Mechanics)

  • Michael Persiianov

    (Moscow Institute of Physics and Technology)

  • Pavel Dvurechensky

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • Alexander Gasnikov

    (Moscow Institute of Physics and Technology
    Skoltech
    Institute of information transmission problems)

  • Dmitry Kovalev

    (Université catholique de Louvain (UCL))

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 observe each time step, and yet, the goal is to average signals (e.g., satellite pictures of some area) by approximating their barycenter. We embed this problem into a class of non-smooth dual-friendly distributed optimization problems over time-varying networks and develop a first-order method for this class. 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. In the experiments, we demonstrate the efficiency of the proposed algorithm when applied to the Wasserstein barycenter problem.

Suggested Citation

  • Olga Yufereva & Michael Persiianov & Pavel Dvurechensky & Alexander Gasnikov & Dmitry Kovalev, 2024. "Decentralized convex optimization on time-varying networks with application to Wasserstein barycenters," Computational Management Science, Springer, vol. 21(1), pages 1-31, June.
    • Handle: RePEc:spr:comgts:v:21:y:2024:i:1:d:10.1007_s10287-023-00493-9
    DOI: 10.1007/s10287-023-00493-9
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    References listed on IDEAS

    as
    1. Eduard Gorbunov & Alexander Rogozin & Aleksandr Beznosikov & Darina Dvinskikh & Alexander Gasnikov, 2022. "Recent Theoretical Advances in Decentralized Distributed Convex Optimization," Springer Optimization and Its Applications, in: Ashkan Nikeghbali & Panos M. Pardalos & Andrei M. Raigorodskii & Michael Th. Rassias (ed.), High-Dimensional Optimization and Probability, pages 253-325, Springer.
    2. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2012. "Double smoothing technique for large-scale linearly constrained convex optimization," LIDAM Reprints CORE 2423, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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