Decentralized Dynamic ADMM with Quantized and Censored Communications

In this paper, we develop a quantized and communication-censored alternating direction method of multipliers (ADMM) to solve a dynamic optimization problem defined over a decentralized network. At every time, the network nodes collaboratively minimize the summation of their local objective functions, which are time-varying. The proposed algorithm, termed as DQC-ADMM, tracks the time-varying optimal solution through local iterative computation and communication. Unlike traditional approaches that require the nodes to transmit the exact local iterates to their neighbors at every time, we quantize the transmitted local iterates and introduce a communication-censoring mechanism so as to reduce the communication cost spent in the optimization process. Although the quantized and censored communications cause inaccuracy, we rigorously prove that the proposed algorithm is able to track the time-varying optimal solution with a bounded error under mild conditions. We also demonstrate the tracking performance and communication savings of the proposed algorithm through numerical experiments.