Asymptotically Optimal Sampling Policy for Quickest Change Detection with Observation-Switching Cost

TL;DR

This paper introduces an asymptotically optimal sampling and stopping strategy for quickest change detection that minimizes observation-switching costs, with proven optimality and practical algorithms.

Contribution

It develops a finite window open-loop sampling policy and a GLR CuSum stopping rule, proving asymptotic optimality and providing algorithms for policy design.

Findings

The proposed policy is asymptotically optimal under certain conditions.

Algorithms are provided with theoretical guarantees for policy optimization.

Empirical results demonstrate improved detection performance in graph signals.

Abstract

We consider the problem of quickest change detection (QCD) in a signal where its observations are obtained using a set of actions, and switching from one action to another comes with a cost. The objective is to design a stopping rule consisting of a sampling policy to determine the sequence of actions used to observe the signal and a stopping time to quickly detect for the change, subject to a constraint on the average observation-switching cost. We propose an open-loop sampling policy of finite window size and a generalized likelihood ratio (GLR) Cumulative Sum (CuSum) stopping time for the QCD problem. We show that the GLR CuSum stopping time is asymptotically optimal with a properly designed sampling policy and formulate the design of this sampling policy as a quadratic programming problem. We prove that it is sufficient to consider policies of window size not more than one when designing policies of finite window size and propose several algorithms that solve this optimization problem with theoretical guarantees. For observation-dependent policies, we propose a $2$-threshold stopping time and an observation-dependent sampling policy. We present a method to design the observation-dependent sampling policy based on open-loop sampling policies. Finally, we apply our approach to the problem of QCD of a partially observed graph signal and empirically demonstrate the performance of our proposed stopping times.