@inproceedings{9f0e1d1bf8144f569ec54f17ce5eab44,
title = "BEER: Fast O(1/T) Rate for Decentralized Nonconvex Optimization with Communication Compression",
abstract = "Communication efficiency has been widely recognized as the bottleneck for large-scale decentralized machine learning applications in multi-agent or federated environments. To tackle the communication bottleneck, there have been many efforts to design communication-compressed algorithms for decentralized nonconvex optimization, where the clients are only allowed to communicate a small amount of quantized information (aka bits) with their neighbors over a predefined graph topology. Despite significant efforts, the state-of-the-art algorithm in the nonconvex setting still suffers from a slower rate of convergence O((G/T)2/3) compared with their uncompressed counterpart, where G measures the data heterogeneity across different clients, and T is the number of communication rounds. This paper proposes BEER, which adopts communication compression with gradient tracking, and shows it converges at a faster rate of O(1/T). This significantly improves over the state-of-the-art rate, by matching the rate without compression even under arbitrary data heterogeneity. Numerical experiments are also provided to corroborate our theory and confirm the practical superiority of BEER in the data heterogeneous regime.",
author = "Haoyu Zhao and Boyue Li and Zhize Li and Peter Richt{\'a}rik and Yuejie Chi",
note = "Funding Information: The work of H. Zhao is supported in part by NSF, ONR, Simons Foundation, DARPA and SRC through awards to S. Arora. The work of B. Li, Z. Li and Y. Chi is supported in part by ONR N00014-19-1-2404, by AFRL under FA8750-20-2-0504, and by NSF under CCF-1901199, CCF-2007911 and CNS-2148212. B. Li is also gratefully supported by Wei Shen and Xuehong Zhang Presidential Fellowship at Carnegie Mellon University. The work of P. Richt{\'a}rik is supported by KAUST Baseline Research Fund. Publisher Copyright: {\textcopyright} 2022 Neural information processing systems foundation. All rights reserved.; 36th Conference on Neural Information Processing Systems, NeurIPS 2022 ; Conference date: 28-11-2022 Through 09-12-2022",
year = "2022",
language = "English (US)",
series = "Advances in Neural Information Processing Systems",
publisher = "Neural information processing systems foundation",
editor = "S. Koyejo and S. Mohamed and A. Agarwal and D. Belgrave and K. Cho and A. Oh",
booktitle = "Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022",
}