Compressed Gradient Tracking for Decentralized Optimization with Linear Convergence

Communication compression techniques are of growing interests in studying the decentralized optimization problem under limited communication, where the global objective is to minimize the average of local cost functions over networked agents using only local computation and peer-to-peer communication. In this paper, we propose a novel compressed gradient tracking algorithm (C-GT) that combines gradient tracking technique with communication compression. We show that C-GT inherits the advantages of gradient tracking-based algorithms, and in particular, achieves linear convergence rate for strongly convex and smooth objective functions. Numerical examples further demonstrate the efficiency and flexibility of the proposed algorithm.