A unified framework for distributed optimization algorithms over time-varying directed graphs
Year: 2021
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Choi, Woocheol, Kim, Doheon, Yun, Seok-Bae
Institutions: Sungkyunkwan University, Korea Institute for Advanced Study
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3192923195