引用本文:李庆海,朱亚楠,刘洪喆.时变不平衡有向图上分布式在线约束优化算法[J].控制理论与应用,2026,43(4):893~904.[点击复制]
LI Qing-hai,ZHU Ya-nan,LIU Hong-zhe.Distributed online constrainted optimization algorithm over time-varying unbalanced digraphs[J].Control Theory & Applications,2026,43(4):893~904.[点击复制]
时变不平衡有向图上分布式在线约束优化算法
Distributed online constrainted optimization algorithm over time-varying unbalanced digraphs
摘要点击 82  全文点击 20  投稿时间：2024-07-22  修订日期：2025-06-21
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DOI编号  10.7641/CTA.2025.40387
  2026,43(4):893-904
中文关键词  分布式在线优化  时变有向图  静态悔界  次线性收敛  非一致性约束
英文关键词  distributed online optimization  time-varying digraphs  static regret  sublinear convergence  nonidentical constraints
基金项目  国家自然科学基金项目(62203224, 62203110, 12302032), 国家自然科学基金–联合基金重点项目(U22B2046)资助.
作者单位E-mail
李庆海 南京信息工程大学 自动化学院 202212490051@nuist.edu.en 
朱亚楠* 南京信息工程大学 自动化学院 ynzhu@nuist.edu.cn 
刘洪喆 东南大学 数学学院  
中文摘要
      本文研究了一类分布式在线约束优化问题, 其中每个智能体局部损失函数时变且为凸函数, 且仅对自身可 知. 各智能体拥有不同的约束集, 且智能体间的通信通过一系列时变不平衡有向图表示. 本文的目标是以分布式方 式求解这一在线优化问题. 针对该问题, 本文在推和的框架下结合投影反馈和消除不平衡性的思想, 提出了一种新 的分布式在线优化算法. 当全局损失函数为强凸时, 证明了算法的网络静态悔界R(T)以速率O(log(T))收敛. 最后, 通过数值仿真实验验证了算法的有效性. 这些结果展示了该算法在解决分布式在线优化问题中的潜在应用前景.
英文摘要
      This paper investigates a class of distributed online constrained optimization problems, where each agent possesses a time-varying convex local loss function that is known only to itself. Each agent operates under a distinct constraint set, and communication between agents is modeled through a series of time-varying unbalanced directed graphs. The goal of this paper is to solve this online optimization problem in a distributed manner. To this end, we propose a novel distributed online optimization algorithm that leverages the push-sum framework and the principles of consensus and projection feedback, while also implementing a strategy to address the issue of imbalance. The theoretical analysis reveals that when the global loss function is strongly convex, the network static regret R(T) of the algorithm converges at a rate of O(log(T)). Finally, the effectiveness of the algorithm is further validated through numerical simulations. These results provide insights into the algorithm’s potential practical value in solving distributed online optimization problems.