Quickest Search for a Change Point

Abstract: This paper considers a sequence of random variables generated according to a common distribution. The distribution might undergo periods of transient changes at an unknown set of time instants, referred to as change-points. The objective is to sequentially collect measurements from the sequence and design a dynamic decision rule for the quickest identification of one change-point in real time, while, in parallel, the rate of false alarms is controlled. This setting is different from the conventional change-point detection settings in which there exists at most one change-point that can be either persistent or transient. The problem is considered under the minimax setting with a constraint on the false alarm rate before the first change occurs. It is proved that the Shewhart test achieves exact optimality under worst-case change points and also worst-case data realization. Numerical evaluations are also provided to assess the performance of the decision rule characterized.