Distributed dual averaging method for multi-agent optimization with quantized communication

In this paper we propose a distributed dual averaging method for solving the constrained multi-agent optimization problem, in which multiple agents try to cooperatively optimize the sum of their local convex objective functions subject to a global convex constraint set over a network. We consider two cases: (i) The communications among agents are perfect, and (ii) The communications among agents are deterministically or probabilistically quantized. In the first case, we provide a way to control the convergence performance of the proposed method through adjusting the number of consensus iterations we run in the subgradient step. In the second case, we consider two kinds of quantizers, and provide bounds on their convergence rates to highlight the dependence on the quantization resolutions respectively. Finally, we provide a numerical example to show the effectiveness of the proposed methods.