Gradient Tracking: A Unified Approach to Smooth Distributed Optimization

Abstract: In this work, we study the classical distributed optimization problem over digraphs, where the objective function is a sum of smooth local functions. Inspired by the implicit tracking mechanism proposed in our earlier work, we develop a unified algorithmic framework from a pure primal perspective, i.e., UGT, which is essentially a generalized gradient tracking method and can unify most existing distributed optimization algorithms with constant step-sizes. It is proved that two variants of UGT can both achieve linear convergence if the global objective function is strongly convex. Finally, the performance of UGT is evaluated by numerical experiments.