Two for the price of one: communication efficient and privacy-preserving distributed average consensus using quantization

Both communication overhead and privacy are main concerns in designing distributed computing algorithms. It is very challenging to address them simultaneously as encryption methods required for privacy-preservation often incur high communication costs. In this paper, we argue that there is a fundamental link between communication efficiency and privacy-preservation through quantization. Based on the observation that quantization, which can save communication bandwidth, will introduce error into the system, we propose a novel privacy-preserving distributed average consensus algorithm which uses the error introduced by quantization as noise to obfuscate the private data for protecting it from being revealed to others. Similar to existing differential privacy based approaches, the proposed approach is robust and has low computational complexity in dealing with two widely considered adversary models: the passive and eavesdropping adversaries. In addition, the method is generally applicable to many distributed optimizers, like PDMM and (generalized) ADMM. We conduct numerical simulations to validate that the proposed approach has superior performance compared to existing algorithms in terms of accuracy, communication bandwidth and privacy.