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Gradient tracking methods have emerged as one of the most popular approachesfor solving decentralized optimization problems over networks. In this setting,each node in the network has a portion of the global objective function, andthe goal is to collectively optimize this function. At every iteration,gradient tracking methods perform two operations (steps): $(1)$ compute localgradients, and $(2)$ communicate information with local neighbors in thenetwork. The complexity of these two steps varies across differentapplications. In this paper, we present a framework that unifies gradienttracking methods and is endowed with flexibility with respect to the number ofcommunication and computation steps. We establish unified theoreticalconvergence results for the algorithmic framework with any composition ofcommunication and computation steps, and quantify the improvements achieved asa result of this flexibility. The framework recovers the results of populargradient tracking methods as special cases, and allows for a direct comparisonof these methods. Finally, we illustrate the performance of the proposedmethods on quadratic functions and binary classification problems.

Balancing Communication and Computation in Gradient Tracking Algorithms for Decentralized Optimization