Sequential Anomaly Detection under a Nonlinear System Cost

We consider the problem of anomaly detection among K heterogeneous processes. At each given time, one process is probed, and the random observations follow two different distributions, depending on whether the process is normal or abnormal. Each anomalous process incurs a cost until its anomaly is identified and fixed, and the cost is a nonlinear (specifically, polynomial with degree d) function of the duration of the anomalous state. The objective is a sequential search strategy that minimizes the total expected cost incurred by all the processes during the detection process under reliability constraints. We propose a search algorithm that consists of exploration, exploitation, and sequential testing phases. We establish its asymptotic optimality and analyze the approximation ratio and the regret under computational constraints.