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arXiv · 2108.02132

A unified framework for distributed optimization algorithms over time-varying directed graphs

Woocheol Choi·Doheon Kim·Seok-Bae Yun
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Abstract

In this paper, we propose a framework under which the decentralized optimization algorithms suggested in \cite{JKJJ,MA, NO,NO2} can be treated in a unified manner. More precisely, we show that the distributed subgradient descent algorithms \cite{JKJJ, NO}, the subgradient-push algorithm \cite{NO2}, and the distributed algorithm with row-stochastic matrix \cite{MA} can be derived by making suitable choices of consensus matrices, step-size and subgradient from the decentralized subgradient descent proposed in \cite{NO}. As a result of such unified understanding, we provide a convergence proof that covers the algorithms in \cite{JKJJ,MA, NO,NO2} under a novel algebraic condition that is strictly weaker than the conventional graph-theoretic condition in \cite{NO}. This unification also enables us to derive a new distributed optimization scheme.

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Woocheol Choi, Doheon Kim, Seok-Bae Yun. 2021-08-04. A unified framework for distributed optimization algorithms over time-varying directed graphs. https://arxiv.org/abs/2108.02132

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