Distributed stochastic gradient tracking methods

• 成果类型: Article
• 署名作者: Pu, Shi; Nedic, Angelia
• 署名单位: The Chinese University of Hong Kong, Shenzhen; Shenzhen Research Institute of Big Data; Arizona State University; Arizona State University-Tempe
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01487-0
• 发表日期: 2021
• 页码: 409-457
• 关键词: convex-optimization; projection algorithms; LEARNING-BEHAVIOR; consensus; CONVERGENCE

摘要

In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method (DSGT) and a gossip-like stochastic gradient tracking method (GSGT). We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant stepsize choice). Under DSGT, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size n, which is a comparable performance to a centralized stochastic gradient algorithm. Moreover, we show that when the network is well-connected, GSGT incurs lower communication cost than DSGT while maintaining a similar computational cost. Numerical example further demonstrates the effectiveness of the proposed methods.