Quantized Distributed Nonconvex Optimization Algorithms With Linear Convergence Under the Polyak-Lojasiewicz Condition

• 成果类型: Article
• 署名作者: Xu, Lei; Yi, Xinlei; Sun, Jiayue; Shi, Yang; Johansson, Karl H.; Yang, Tao
• 署名单位: Northeastern University - China; University of Victoria; Tongji University; Royal Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3563431
• 发表日期: 2025
• 页码: 6853-6860
• 关键词: convergence; cost function; Quantization (signal); Distributed algorithms; vectors; Decoding; Distributed databases; training; sun; Mechanical engineering; Distributed nonconvex optimization; linear convergence; Polyak-Lojasiewicz (P-L) condition; quantized communication

摘要

This article considers distributed optimization for minimizing the average of local nonconvex cost functions, by using local information exchange over undirected communication networks. To reduce the required communication capacity, we introduce an encoder-decoder scheme. By integrating it with distributed gradient tracking and proportional integral algorithms, respectively, we then propose two quantized distributed nonconvex optimization algorithms. Assuming the global cost function satisfies the Polyak-Lojasiewicz condition, which does not require the global cost function to be convex and the global minimizer is not necessarily unique, we show that our proposed algorithms linearly converge to a global optimal point. Moreover, we show that a low data rate is sufficient to guarantee linear convergence when the algorithm parameters are properly chosen. The theoretical results are illustrated by numerical examples.