An Accelerated Distributed Online Gradient Push-Sum Algorithm in Time-varying Networks

Abstract

This paper investigates an online convex optimization problem 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 global cost function. To tackle such optimization problems, an accelerated distributed online gradient push-sum algorithm is firstly proposed, which combines the momentum acceleration technique and 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 an improved rate with order of $\mathcal{O}\left( {\sqrt {1 + \log T} } \right)$, 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 demonstrate the effectiveness of the proposed algorithm.