Privacy-Aware Quickest Change Detection

This paper considers the problem of the quickest detection of a change in distribution while taking privacy considerations into account. Our goal is to sanitize the signal to satisfy information privacy requirements while being able to detect a change quickly. We formulate the privacy-aware quickest change detection (QCD) problem by including a privacy constraint to Lorden's minimax formulation. We show that the Generalized Likelihood Ratio (GLR) CuSum achieves asymptotic optimality with a properly designed sanitization channel and formulate the design of this sanitization channel as an optimization problem. For computational tractability, a continuous relaxation for the discrete counting constraint is proposed and the augmented Lagrangian method is applied to obtain locally optimal solutions.