Privacy Preserving Average Consensus Through Network Augmentation

Average consensus protocols play a central role in distributed systems and decision-making such as distributed information fusion, distributed optimization, distributed estimation, and control. A key advantage of these protocols is that agents exchange and reveal their state information only to their neighbors. In its basic form, the goal of average consensus protocols is to compute an aggregate such as average of network data; however, existing protocols could lead to leakage of individual agent data thus leading to privacy concerns in scenarios involving sensitive information. In this paper, we propose novel (noiseless) privacy preserving distributed algorithms for multi-agent systems to reach average consensus. The main idea of the algorithms is that each agent runs a (small) network with a carefully crafted structure and dynamics to form a network of networks that conforms to the inter-agent connectivity imposed by the agent communication graph. Together with a re-weighting of the dynamic parameters dictating the inter-agent dynamics and the initial states, we show that it is possible to ensure that agent values reach appropriate consensus, while ensuring privacy of individual agent data. Furthermore, we show that, under mild assumptions, it is possible to design networks with similar characteristics in a distributed fashion. Finally, we illustrate the proposed schemes in a variety of example scenarios.