Quantized Distributed Gradient Tracking Algorithm With Linear Convergence in Directed Networks

• 成果类型: Article
• 署名作者: Xiong, Yongyang; Wu, Ligang; You, Keyou; Xie, Lihua
• 署名单位: Tsinghua University; Harbin Institute of Technology; Nanyang Technological University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3219289
• 发表日期: 2023
• 页码: 5638-5645
• 关键词: Directed networks; distributed optimization; gra-dient tracking algorithm; quantized communication

摘要

Communication efficiency is a major bottleneck in the applications of distributed networks. To address the problem, the problem of quantized distributed optimization has attracted a lot of attention. However, most of the existing quantized distributed optimization algorithms can only converge sublinearly. To achieve linear convergence, this article proposes a novel quantized distributed gradient tracking algorithm (Q-DGT) to minimize a finite sum of local objective functions over directed networks. Moreover, we explicitly derive lower bounds for the number of quantization levels, and prove that Q-DGT can converge linearly even when the exchanged variables are respectively quantized with three quantization levels. Numerical results also confirm the efficiency of the proposed algorithm.