Communication compression techniques are of growing interests for solving the decentralized optimization problem under limited communication, where the global objective is to minimize the average of local cost functions over a multi-agent network 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. In particular, C-GT is compatible with a general class of compression operators that unifies both unbiased and biased compressors. We show that C-GT inherits the advantages of gradient tracking-based algorithms and achieves linear convergence rate for strongly convex and smooth objective functions. Numerical examples complement the theoretical findings and demonstrate the efficiency and flexibility of the proposed algorithm.
@article{arxiv.2205.12623,
title = {A Compressed Gradient Tracking Method for Decentralized Optimization with Linear Convergence},
author = {Yiwei Liao and Zhuorui Li and Kun Huang and Shi Pu},
journal= {arXiv preprint arXiv:2205.12623},
year = {2022}
}
Comments
To appear in TAC. arXiv admin note: substantial text overlap with arXiv:2103.13748