  Decentralized methods to solve finite-sum minimization problems are important
in many signal processing and machine learning tasks where the data is
distributed over a network of nodes and raw data sharing is not permitted due
to privacy and/or resource constraints. In this article, we review
decentralized stochastic first-order methods and provide a unified algorithmic
framework that combines variance-reduction with gradient tracking to achieve
both robust performance and fast convergence. We provide explicit theoretical
guarantees of the corresponding methods when the objective functions are smooth
and strongly-convex, and show their applicability to non-convex problems via
numerical experiments. Throughout the article, we provide intuitive
illustrations of the main technical ideas by casting appropriate tradeoffs and
comparisons among the methods of interest and by highlighting applications to
decentralized training of machine learning models.
