Sequential Anomaly Detection With Observation Control

The problem of anomaly detection is considered when multiple processes are observed sequentially, but it is possible to sample only a subset of them at a time according to an adaptive sampling policy. The problem is to stop sampling as soon as possible and identify the anomalous processes, while controlling appropriate error probabilities. We consider two versions of this problem: in the first one there is no assumption regarding the anomalous processes, in the second their number is assumed to be known a priori. For each version, we obtain the optimal asymptotic performance as the error probabilities vanish and characterize the sampling rules that lead to asymptotic optimality. Moreover, we present two sampling rules for each setup, which differ in terms of the computational complexity and the actual performance they imply.