An introduction to decentralized stochastic optimization with gradient tracking
This is an incremental review article summarizing existing methods for decentralized optimization in signal processing, control, and machine learning applications.
The paper reviews decentralized stochastic first-order optimization methods for finite-sum minimization problems where data is distributed across networks with communication/privacy constraints, focusing on recent improvements using gradient tracking and variance reduction for smooth strongly-convex functions.
Decentralized solutions to finite-sum minimization are of significant importance in many signal processing, control, and machine learning applications. In such settings, the data is distributed over a network of arbitrarily-connected nodes and raw data sharing is prohibitive often due to communication or privacy constraints. In this article, we review decentralized stochastic first-order optimization methods and illustrate some recent improvements based on gradient tracking and variance reduction, focusing particularly on smooth and strongly-convex objective functions. We provide intuitive illustrations of the main technical ideas as well as applications of the algorithms in the context of decentralized training of machine learning models.