Distributed Online Optimization With Long-Term Constraints

• 成果类型: Article
• 署名作者: Yuan, Deming; Proutiere, Alexandre; Shi, Guodong
• 署名单位: Nanjing University of Science & Technology; Royal Institute of Technology; University of Sydney
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3057601
• 发表日期: 2022
• 页码: 1089-1104
• 关键词: Absolute constraint violation; distributed online convex optimization (DOCO); long-term constraints; one-point bandit feedback; regret

摘要

In this article, we consider distributed online convex optimization problems, where the distributed system consists of various computing units connected through a time-varying communication graph. In each time step, each computing unit selects a constrained vector, experiences a loss equal to an arbitrary convex function evaluated at this vector, and may communicate to its neighbors in the graph. The objective is to minimize the system-wide loss accumulated over time. We propose a decentralized algorithm with regret and cumulative constraint violation in O(T-max{c,T-1-c}) and O(T1-c/2), respectively, for any c is an element of (0, 1), where T is the time horizon. When the loss functions are strongly convex, we establish improved regret and constraint violation upper bounds in O(log(T)) and O(root T log(T)). These regret scalings match those obtained by state-of-the-art algorithms and fundamental limits in the corresponding centralized online optimization problem (for both convex and strongly convex loss functions). In the case of bandit feedback, the proposed algorithms achieve a regret and constraint violation in O(T-max{c,T-1-c/3}) and O(T1-c/2) for any c is an element of (0, 1). We numerically illustrate the performance of our algorithms for the particular case of distributed online regularized linear regression problems on synthetic and real data.