In the modern paradigm of multi-agent networks, communication has become one of the main bottlenecks for decentralized optimization, where a large number of agents are involved in minimizing the average of the local cost functions. In this paper, we propose a robust compressed push-pull algorithm (RCPP) that combines gradient tracking with communication compression. In particular, RCPP is compatible with a much more general class of compression operators that allow both relative and absolute compression errors. We show that RCPP achieves linear convergence rate for smooth objective functions satisfying the Polyak-{\L}ojasiewicz condition over general directed networks. Numerical examples verify the theoretical findings and demonstrate the efficiency, flexibility, and robustness of the proposed algorithm.
@article{arxiv.2303.07091,
title = {A Linearly Convergent Robust Compressed Push-Pull Method for Decentralized Optimization},
author = {Yiwei Liao and Zhuorui Li and Shi Pu},
journal= {arXiv preprint arXiv:2303.07091},
year = {2023}
}