Device Selection of Distributed Primal-Dual Algorithms Over Wireless Networks

In this paper, the implementation of a distributed primal-dual learning algorithm over realistic wireless networks is investigated. In the considered model, the users and one base station (BS) cooperatively perform a distributed primal-dual learning algorithm for controlling and optimizing wireless networks. In particular, each user must locally update the primal and dual variables and send the updated primal variables to the BS. The BS aggregates the received primal variables and broadcasts the aggregated variables to all users. Since all of the primal and dual variables as well as aggregated variables are transmitted over wireless links, the imperfect wireless links will affect the solution achieved by the distributed primal-dual algorithm. Therefore, it is necessary to study how wireless factors such as transmission errors affect the implementation of the distributed primal-dual algorithm and how to optimize wireless network performance to improve the solution achieved by the distributed primal-dual algorithm. To address these challenges, the convergence rate of the primal-dual algorithm is provided in a closed form while considering the impact of wireless factors such as data transmission errors. Simulation results show that the proposed distributed primal-dual algorithm can reduce the gap between the target and obtained solution compared to the distributed primal-dual learning algorithm without considering imperfect wireless transmission.