Active Anomaly Detection with Switching Cost

The problem of detecting a single anomalous process among multiple independent processes is considered. Under a constraint on the number of processes that can be probed simultaneously, the decision maker should decide which processes to probe at each time and when to terminate the probing. Compared with previous work considering only the observation costs, the switching costs of switchings across processes also need to be taken into account in many practical scenarios. The objective is an active inference strategy that minimizes the Bayesian risk taking into account of the sample complexity, switching cost, as well as detection errors. Based on the framework of sequential design of experiments, we propose a low-complexity, low-switching deterministic policy for two scenarios where the total switching cost is negligible and the total switching cost is comparable to the total observation cost. We show that the proposed algorithm is asymptotically optimal in the former scenario and is order optimal in the latter scenario. Simulation results demonstrate strong performance in the finite regime for both scenarios.