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

Minimum-norm Sparse Perturbations for Opacity in Linear Systems

Opacity is a notion that describes an eavesdropper's inability to estimate a system's 'secret' states by observing the system's outputs. In this paper, we propose algorithms to compute the minimum sparse perturbation to be added to a system to make its initial states opaque. For these perturbations, we consider two sparsity constraints - structured and affine. We develop an algorithm to compute the global minimum-norm perturbation for the structured case. For the affine case, we use the global minimum solution of the structured case as initial point to compute a local minimum. Empirically, this local minimum is very close to the global minimum. We demonstrate our results via a running example.Comment: Submitted to Indian Control Conference, 2023 (6 pages

A Design Framework for Strongly χ2\chi^2-Private Data Disclosure

In this paper, we study a stochastic disclosure control problem using information-theoretic methods. The useful data to be disclosed depend on private data that should be protected. Thus, we design a privacy mechanism to produce new data which maximizes the disclosed information about the useful data under a strong $\chi^2$-privacy criterion. For sufficiently small leakage, the privacy mechanism design problem can be geometrically studied in the space of probability distributions by a local approximation of the mutual information. By using methods from Euclidean information geometry, the original highly challenging optimization problem can be reduced to a problem of finding the principal right-singular vector of a matrix, which characterizes the optimal privacy mechanism. In two extensions we first consider a scenario where an adversary receives a noisy version of the user's message and then we look for a mechanism which finds $U$ based on observing $X$, maximizing the mutual information between $U$ and $Y$ while satisfying the privacy criterion on $U$ and $Z$ under the Markov chain $(Z,Y)-X-U$.Comment: 16 pages, 2 figure