Distributed Optimization Under Unbalanced Digraphs With Node Errors: Robustness of Surplus-Based Dual Averaging Algorithm

• Published in: IEEE transactions on control of network systems Vol. 8; no. 1; pp. 331 - 341
• Main Authors: Shi, Chong-Xiao, Yang, Guang-Hong
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.03.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additives; Algorithms; Attenuation; Control systems; Convergence; Distributed constrained optimization; Gradient methods; Graph theory; Multiagent systems; node errors; Nodes; Optimization; Protocols; Random processes; Robustness; unbalanced digraphs
• ISSN: 2325-5870; 2372-2533
• DOI: 10.1109/TCNS.2020.3011837

In this article, the robustness of distributed constrained optimization algorithms for weight-unbalanced directed multiagent networks is studied. Specifically, it is assumed that each agent is subject to additive random node errors , which are caused by the imperfect communication in networks. Under this framework, it is shown that a typical algorithm, called surplus-based dual averaging (SDA), can successfully achieve the convergence to the optimal value of the considered optimization problem, which exhibits the robustness to the node errors. Technically, in the proof of this result, an important augmentation of the node errors in the fusion and surplus variables is first introduced, and then by means of the random process theory and the attenuation effect of diminishing step size on node errors, the robustness of SDA is proved. In addition, inspired by the SDA, a robust algorithm is developed to solve the distributed online optimization problem with node errors. Finally, simulations are given to verify the theoretical results.