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Decentralized methods to solve finite-sum minimization problems are importantin many signal processing and machine learning tasks where the data isdistributed over a network of nodes and raw data sharing is not permitted dueto privacy and/or resource constraints. In this article, we reviewdecentralized stochastic first-order methods and provide a unified algorithmicframework that combines variance-reduction with gradient tracking to achieveboth robust performance and fast convergence. We provide explicit theoreticalguarantees of the corresponding methods when the objective functions are smoothand strongly-convex, and show their applicability to non-convex problems vianumerical experiments. Throughout the article, we provide intuitiveillustrations of the main technical ideas by casting appropriate tradeoffs andcomparisons among the methods of interest and by highlighting applications todecentralized training of machine learning models.

Gradient tracking and variance reduction for decentralized optimization and machine learning