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Non-smooth setting of stochastic decentralized convex optimization problem over time-varying Graphs

Author

Listed:
  • Aleksandr Lobanov

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

  • Andrew Veprikov

    (Moscow Institute of Physics and Technology)

  • Georgiy Konin

    (Moscow Institute of Physics and Technology)

  • Aleksandr Beznosikov

    (Moscow Institute of Physics and Technology
    Skoltech
    Institute for Information Transmission Problems)

  • Alexander Gasnikov

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

  • Dmitry Kovalev

    (Universite Catholique de Louvain)

Abstract

Distributed optimization has a rich history. It has demonstrated its effectiveness in many machine learning applications, etc. In this paper we study a subclass of distributed optimization, namely decentralized optimization in a non-smooth setting. Decentralized means that m agents (machines) working in parallel on one problem communicate only with the neighbors agents (machines), i.e. there is no (central) server through which agents communicate. And by non-smooth setting we mean that each agent has a convex stochastic non-smooth function, that is, agents can hold and communicate information only about the value of the objective function, which corresponds to a gradient-free oracle. In this paper, to minimize the global objective function, which consists of the sum of the functions of each agent, we create a gradient-free algorithm by applying a smoothing scheme via $$l_2$$ l 2 randomization. We also verify in experiments the obtained theoretical convergence results of the gradient-free algorithm proposed in this paper.

Suggested Citation

  • Aleksandr Lobanov & Andrew Veprikov & Georgiy Konin & Aleksandr Beznosikov & Alexander Gasnikov & Dmitry Kovalev, 2023. "Non-smooth setting of stochastic decentralized convex optimization problem over time-varying Graphs," Computational Management Science, Springer, vol. 20(1), pages 1-55, December.
    • Handle: RePEc:spr:comgts:v:20:y:2023:i:1:d:10.1007_s10287-023-00479-7
    DOI: 10.1007/s10287-023-00479-7
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