Optimal Privacy-Aware Dynamic Estimation

In this paper, we develop an information-theoretic framework for the optimal privacy-aware estimation of the states of a (linear or nonlinear) system. In our setup, a private process, modeled as a first-order Markov chain, derives the states of the system, and the state estimates are shared with an untrusted party who might attempt to infer the private process based on the state estimates. As the privacy metric, we use the mutual information between the private process and the state estimates. We first show that the privacy-aware estimation is a closed-loop control problem wherein the estimator controls the belief of the adversary about the private process. We also derive the Bellman optimality principle for the optimal privacy-aware estimation problem, which is used to study the structural properties of the optimal estimator. We next develop a policy gradient algorithm, for computing an optimal estimation policy, based on a novel variational formulation of the mutual information. We finally study the performance of the optimal estimator in a building automation application.