Differentially Private Distributed Parameter Estimation

Data privacy is an important issue in control systems, especially when datasets contain sensitive information about individuals. In this paper, the authors are concerned with the differentially private distributed parameter estimation problem, that is, we estimate an unknown parameter while protecting the sensitive information of each agent. First, the authors propose a distributed stochastic approximation estimation algorithm in the form of the differentially private consensus+innovations (DP-CI), and establish the privacy and convergence property of the proposed algorithm. Specifically, it is shown that the proposed algorithm asymptotically unbiased converges in mean-square to the unknown parameter while differential privacy-preserving holds for finite number of iterations. Then, the exponentially damping step-size and privacy noise for DP-CI algorithm is given. The estimate approximately converges to the unknown parameter with an error proportional to the step-size parameter while differential privacy-preserving holds for all iterations. The tradeoff between accuracy and privacy of the algorithm is effectively shown. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithm.