Searching for Anomalies with Multiple Plays under Delay and Switching Costs

The problem of searching for L anomalous processes among M processes is considered. At each time, the decision maker can observe a subset of K processes (i.e., multiple plays). The measurement drawn when observing a process follows one of two different distributions, depending whether the process is normal or abnormal. The goal is to design a policy that minimizes the Bayes risk which balances between the sample complexity, detection errors, and the switching cost associated with switching across processes. We develop a policy, dubbed consecutive controlled sensing (CCS), to achieve this goal. We prove theoretically that CCS is asymptotically optimal in terms of minimizing the Bayes risk as the sample complexity approaches infinity. Simulation results demonstrate strong performance of CCS in the finite regime as well.