Online Distributed Optimization With Nonconvex Objective Functions: Sublinearity of First-Order Optimality Condition-Based Regret

• 成果类型: Article
• 署名作者: Lu, Kaihong; Wang, Long
• 署名单位: Jiangsu University; Peking University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3091096
• 发表日期: 2022
• 页码: 3029-3035
• 关键词: Optimization; linear programming; Distributed algorithms; Convex functions; mirrors; STANDARDS; Mathematical model; Distributed nonconvex optimization; multiagent systems (MASs); online optimization

摘要

In this article, the problem of online distributed optimization with a set constraint is solved by employing a network of agents. Each agent only has access to a local objective function and set constraint, and can only communicate with its neighbors via a digraph, which is not necessarily balanced. Moreover, agents do not have prior knowledge of their future objective functions. Different from existing works on online distributed optimization, we consider the scenario, where objective functions at each time step are nonconvex. To handle this challenge, we propose an online distributed algorithm based on the consensus algorithm and the mirror descent algorithm. Of particular interest is that regrets involving first-order optimality condition are used to measure the performance of the proposed algorithm. Under mild assumptions on the communication graph and objective functions, we prove that regrets grow sublinearly. Finally, a simulation example is worked out to demonstrate the effectiveness of our theoretical results.