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In this paper we extend the Shiryaev's quickest change detection formulationby also accounting for the cost of observations used before the change point.The observation cost is captured through the average number of observationsused in the detection process before the change occurs. The objective is toselect an on-off observation control policy, that decides whether or not totake a given observation, along with the stopping time at which the change isdeclared, so as to minimize the average detection delay, subject to constraintson both the probability of false alarm and the observation cost. By consideringa Lagrangian relaxation of the constraint problem, and using dynamicprogramming arguments, we obtain an \textit{a posteriori} probability basedtwo-threshold algorithm that is a generalized version of the classical Shiryaevalgorithm. We provide an asymptotic analysis of the two-threshold algorithm andshow that the algorithm is asymptotically optimal, i.e., the performance of thetwo-threshold algorithm approaches that of the Shiryaev algorithm, for a fixedobservation cost, as the probability of false alarm goes to zero. We also show,using simulations, that the two-threshold algorithm has good observationcost-delay trade-off curves, and provides significant reduction in observationcost as compared to the naive approach of fractional sampling, where samplesare skipped randomly. Our analysis reveals that, for practical choices ofconstraints, the two thresholds can be set independent of each other: one basedon the constraint of false alarm and another based on the observation costconstraint alone.

Data-Efficient Quickest Change Detection with On-Off Observation Control