Quickest Change Detection with Privacy Constraint

TL;DR

This paper addresses the challenge of designing privacy-preserving signal sanitization methods for quickest change detection, demonstrating asymptotic optimality of GLR CuSum with new algorithms for channel design.

Contribution

It introduces a framework for privacy-aware quickest change detection, proposing relaxations and algorithms for optimal sanitization channel design under centralized and decentralized settings.

Findings

GLR CuSum achieves asymptotic optimality with proper sanitization.

Proposed relaxations enable practical solutions for the sanitization design.

Algorithms are developed for both centralized and decentralized privacy-aware QCD.

Abstract

This paper considers Lorden's minimax quickest change detection (QCD) problem with a privacy constraint. The goal is to sanitize a signal to satisfy inference privacy requirements while being able to detect a change quickly. We show that the Generalized Likelihood Ratio (GLR) CuSum achieves asymptotic optimality with a properly designed sanitization channel. We formulate the design of this sanitization channel as an optimization problem, which is however challenging to solve. We propose relaxations to the optimization problem and develop algorithms to obtain a solution. We also consider the privacy-aware QCD problem under a decentralized framework and propose algorithms to solve the relaxed channel design problem under this framework.