Differentially Private Average Consensus with Optimal Noise Selection

This paper studies the problem of privacy-preserving average consensus in multi-agent systems. The network objective is to compute the average of the initial agent states while keeping these values differentially private against an adversary that has access to all interagent messages. We establish an impossibility result that shows that exact average consensus cannot be achieved by any algorithm that preserves differential privacy. This result motives our design of a differentially private discrete-time distributed algorithm that corrupts messages with Laplacian noise and is guaranteed to achieve average consensus in expectation. We examine how to optimally select the noise parameters in order to minimize the variance of the network convergence point for a desired level of privacy.