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

Abstract

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  ( √ T) , 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.

Resilient algorithm for distributed resource allocation under false data injection attacks

“…which is a perturbed system with nonvanishing perturbation 𝜈 ′ (t). Similar to the analysis of system (12), the derivative of V along the trajectories of perturbed system (18) satisfies…”

“…In recent years, the results of asymptotic and exponential convergence of distributed resource allocation algorithms have been obtained for agents communicating on undirected graphs [9][10][11][12][13][14][15]. And the related results were also extended to weight-(un)balanced directed graphs (digraphs) and switching networks [16][17][18][19][20]. In addition to the asymptotic and exponential convergence results, recent work dealt with finite-time and predefine-time convergence of distributed algorithms [21][22][23].…”

A Survey on Distributed Online Optimization and Game

“…Moreover, some accelerated and improved methods, such as Nesterov accelerated gradient method and adaptive gradient methods, have been leveraged to further improve the performance. For example, the momentum acceleration technique was exploited to improve the performance under time-varying unbalanced communication graphs in [128], where an improved static regret bound O( √ 1 + log T + √ T ) is established for convex cost functions. Also, adaptive gradient methods have been integrated into DOL in [129]- [131].…”