| 内容提要: |
This paper studies the multi-agent average consensus problem under the requirement of differential
privacy of the agents’ initial states against an adversary that has access to all the messages. We first
establish that a differentially private consensus algorithm cannot guarantee convergence of the agents’
states to the exact average in distribution, which in turn implies the same impossibility for other stronger
notions of convergence. This result motivates our design of a novel differentially private Laplacian
consensus algorithm in which agents linearly perturb their state-transition and message-generating
functions with exponentially decaying Laplace noise. We prove that our algorithm converges almost
surely to an unbiased estimate of the average of agents’ initial states, compute the exponential meansquare
rate of convergence, and formally characterize its differential privacy properties.Weshow that the
optimal choice of our design parameters (with respect to the variance of the convergence point around
the exact average) corresponds to a one-shot perturbation of initial states and compare our design with
various counterparts from the literature. Simulations illustrate our results. |