Optimal Privacy-Aware Dynamic Estimation

TL;DR

This paper introduces an information-theoretic framework for designing optimal estimators that balance accurate state estimation with privacy preservation against untrusted parties, using a control-theoretic approach and policy gradient methods.

Contribution

It formulates privacy-aware estimation as a control problem, derives the Bellman optimality principle, and develops a policy gradient algorithm based on a new variational mutual information formulation.

Findings

The framework effectively balances estimation accuracy and privacy.

The Bellman equation characterizes the structure of optimal estimators.

The policy gradient algorithm computes near-optimal privacy-preserving policies.

Abstract

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.