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arXiv · 2303.07091

A Linearly Convergent Robust Compressed Push-Pull Method for Decentralized Optimization

Yiwei Liao·Zhuorui Li·Shi Pu
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Abstract

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.

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Yiwei Liao, Zhuorui Li, Shi Pu. 2023-03-13. A Linearly Convergent Robust Compressed Push-Pull Method for Decentralized Optimization. https://arxiv.org/abs/2303.07091

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