Distributed Stochastic Optimization Under a General Variance Condition

• 成果类型: Article
• 署名作者: Huang, Kun; Li, Xiao; Pu, Shi
• 署名单位: The Chinese University of Hong Kong, Shenzhen
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3393169
• 发表日期: 2024
• 页码: 6105-6120
• 关键词: Optimization; linear programming; Distributed databases; gradient methods; CONVERGENCE; Complexity theory; Particle measurements; distributed optimization; Nonconvex Optimization; stochastic optimization

摘要

Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Although numerous algorithms have been proposed and successfully applied to general practical problems, their theoretical guarantees mainly rely on certain boundedness conditions on the stochastic gradients, varying from uniform boundedness to the relaxed growth condition. In addition, how to characterize the data heterogeneity among the agents and its impacts on the algorithmic performance remains challenging. In light of such motivations, we revisit the classical federated averaging algorithm (McMahan et al., 2017) as well as the more recent SCAFFOLD method (Karimireddy et al., 2020) for solving the distributed stochastic optimization problem and establish the convergence results under only a mild variance condition on the stochastic gradients for smooth nonconvex objective functions. Almost sure convergence to a stationary point is also established under the condition. Moreover, we discuss a more informative measurement for data heterogeneity as well as its implications.