Asymptotically Optimal Anomaly Detection via Sequential Testing

Sequential detection of independent anomalous processes among K processes is considered. At each time, only M (1 ≤ M ≤ K) processes can be observed, and the observations from each chosen process follow two different distributions, depending on whether the process is normal or abnormal. Each anomalous process incurs a cost per unit time until its anomaly is identified and fixed. Switching across processes and state declarations are allowed at all times, while decisions are based on all past observations and actions. 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 develop index-type algorithms for the case with both known observation distributions and the case when the observation distributions have unknown parameters. We show that the proposed algorithms are asymptotically optimal in terms of minimizing the total expected cost as the error constraints approach zero. Simulation results demonstrate strong performance in the finite regime.