Asymptotically Optimal Sampling Policy for Quickest Change Detection with Observation-Switching Cost
share
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 a 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 length and propose several algorithms that solve this optimization problem with theoretical guarantees. Finally, we apply our approach to the problem of QCD of a partially observed graph signal.
READ FULL TEXT