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arXiv · 2307.00392

Non-Smooth Setting of Stochastic Decentralized Convex Optimization Problem Over Time-Varying Graphs

Aleksandr Lobanov·Andrew Veprikov·Georgiy Konin·Aleksandr Beznosikov·Alexander Gasnikov·Dmitry Kovalev
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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 $l_2$ randomization. We also verify in experiments the obtained theoretical convergence results of the gradient-free algorithm proposed in this paper.

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Aleksandr Lobanov, Andrew Veprikov, Georgiy Konin, Aleksandr Beznosikov, Alexander Gasnikov, Dmitry Kovalev. 2023-07-01. Non-Smooth Setting of Stochastic Decentralized Convex Optimization Problem Over Time-Varying Graphs. https://doi.org/10.1007/s10287-023-00479-7

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