A flexible gradient tracking algorithmic framework for decentralized optimization

In decentralized optimization over networks, each node in the network has a portion of the global objective function and the aim is to collectively optimize this function. Gradient tracking methods have emerged as a popular alternative for solving such problems due to their strong theoretical guarantees and robust empirical performance. These methods perform two operations (steps) at each iteration: (1) compute local gradients at each node, and (2) communicate local information with neighboring nodes. The complexity of these two steps can vary significantly across applications. In this work, we present a flexible gradient tracking algorithmic framework designed to balance the composition of communication and computation steps over the optimization process using a randomized scheme. The proposed framework is general, unifies gradient tracking methods, and recovers classical gradient tracking methods as special cases. We establish convergence guarantees in expectation and illustrate how the complexity of communication and computation steps can be balanced using the provided flexibility. Finally, we illustrate the performance of the proposed methods on quadratic and logistic regression problems, and compare against popular algorithms from the literature.