Quickest anomaly detection: A case of active hypothesis testing

The problem of quickest detection of an anomalous process among M processes is considered. At each time, a subset of the processes can be observed, and the observations follow two different distributions, depending on whether the process is normal or abnormal. The objective is a sequential search strategy that minimizes the expected detection time subject to an error probability constraint. This problem can be considered as a special case of active hypothesis testing first considered by Chernoff in 1959, where a randomized test was proposed and shown to be asymptotically optimal. For the special case considered in this paper, we show that a simple deterministic test achieves asymptotic optimality and offers better performance in the finite regime.