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

Aleksandr Lobanov (), Andrew Veprikov (), Georgiy Konin (), Aleksandr Beznosikov (), Alexander Gasnikov () and Dmitry Kovalev ()
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Aleksandr Lobanov: Moscow Institute of Physics and Technology
Andrew Veprikov: Moscow Institute of Physics and Technology
Georgiy Konin: Moscow Institute of Physics and Technology
Aleksandr Beznosikov: Moscow Institute of Physics and Technology
Alexander Gasnikov: Moscow Institute of Physics and Technology
Dmitry Kovalev: Universite Catholique de Louvain

Computational Management Science, 2023, vol. 20, issue 1, No 48, 55 pages

Abstract: 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.

Keywords: Stochastic Accelerated Decentralized Optimization Method; Time-varying graphs; Non-smooth opimization; Gradient-free algorithms (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10287-023-00479-7

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