An accelerated distributed online gradient push‐sum algorithm on time‐varying directed networks

• Published in: Asian journal of control Vol. 24; no. 6; pp. 3278 - 3288
• Main Authors: Fang, Runyue, Li, Dequan, Shen, Xiuyu, Zhou, Yuejin
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc 01.11.2022
• Subjects: Algorithms; Cost function; distributed convex optimization; momentum acceleration; Networks; online convex optimization; Optimization; time‐varying directed network
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.2721

This paper investigates a distributed online optimization problem with convex objective functions on time‐varying directed networks, where each agent holds its own convex cost function and the goal is to cooperatively minimize the sum of the local cost functions. To tackle such optimization problems, an accelerated distributed online gradient push‐sum algorithm is firstly proposed, which combines the momentum acceleration technique and the push‐sum strategy. Then, we specifically analyze the regret for the proposed algorithm. The theoretical result shows that the individual regret of the proposed algorithm achieves a sublinear regret with order of OT, where T is the time horizon. Moreover, we implement the proposed algorithm in sensor networks for solving the distributed online estimation problem, and the results illustrate the effectiveness of the proposed algorithm.