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