A Compressed Gradient Tracking Method for Decentralized Optimization With Linear Convergence

• 成果类型: Article
• 署名作者: Liao, Yiwei; Li, Zhuorui; Huang, Kun; Pu, Shi
• 署名单位: The Chinese University of Hong Kong, Shenzhen; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Shenzhen Research Institute of Big Data; Shenzhen Research Institute of Big Data; The Chinese University of Hong Kong, Shenzhen; Shenzhen Institute of Artificial Intelligence & Robotics for Society; The Chinese University of Hong Kong, Shenzhen
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3180695
• 发表日期: 2022
• 页码: 5622-5629
• 关键词: linear programming; CONVERGENCE; Compressors; Quantization (signal); cost function; robots; Radio frequency; Communication compression; decentralized optimization; gradient tracking; linear convergence

摘要

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 multiagent network using only local computation and peer-to-peer communication. In this article, 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.