Asymptotically Optimal Search for a Change Point Anomaly Under a Composite Hypothesis Model

We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common distribution with an unknown parameter (vector). This parameter belongs to either a normal or an abnormal space depending on the current state of the process. Before the change point, all processes, including the anomalous one, are in a normal state; after the change point, the anomalous process transitions to an abnormal state. Our goal is to design a sequential search strategy that minimizes the Bayes risk by balancing sample complexity and detection accuracy. We propose a deterministic search algorithm that alternates between exploration and exploitation phases to efficiently identify the anomalous process. We rigorously analyze its performance under both the case of known normal parameters, and the case where all parameters are unknown. In both settings, we establish asymptotic optimality of the proposed algorithm in minimizing the Bayes risk as the error probability vanishes. The notion of optimality aligns with standard performance bench-marks in each setting, accounting for differences in available information and the associated fundamental limits. Simulation results are presented to validate the theoretical findings.