Quantized Gradient Descent Algorithm for Distributed Nonconvex Optimization

Abstract

This paper presents a quantized gradient descent algorithm for distributed nonconvex optimization in multiagent systems that takes into account the bandwidth limitation of communication channels. Each agent encodes its estimation variable using a zoom-in parameter and sends the quantized intermediate variable to the neighboring agents. Then, each agent updates the estimation by decoding the received information. In this paper, we show that all agents achieve consensus and their estimated variables converge to a critical point in the optimization problem. A numerical example of a nonconvex logistic regression shows that there is a trade-off between the convergence rate of the estimation and the communication bandwidth.