Average Consensus for Expressed and Private Opinions
Jing Zhang, Jianquan Lu, Christoforos N. Hadjicostis
Abstract
In this paper, we study the problem of privacy-preserving average consensus from a different perspective. Previous research has mainly focused on designing privacy augmentation mechanisms for classical average consensus algorithms, which can lead to overhead (in the form of parameters exchanged between agents or extra privacy operations). Motivated by the framework on expressed and private opinions within social networks, we propose an alternative iterative algorithm to simultaneously update two state variables. One of these variables is used to transmit and interact among the network, while the other variable represents the real state evolution of agents and is not directly visible to other agents. We demonstrate that the algorithm can achieve the same performance as the well-known Laplacian consensus algorithm, but without the added overhead of extra privacy protection operations. Furthermore, our algorithm is viable on general strongly connected digraphs, and does not require the topology to be undirected or balanced, nor does it require nodes to know their out-neighbors, thus greatly weakening the topological requirements. Finally, we validate the effectiveness of the proposed algorithm via numerical simulations.