Learning to Detect an Anomalous Target with Observations from an Exponential Family

The problem of identifying an anomalous arm from a set of K arms, with fixed confidence, is studied in a sequential decision-making scenario. Each arm's signal follows a distribution from the vector parameter exponential family. The actual parameters of the anomalous and regular arms are unknown. Further, the decision maker incurs a cost for switching from one arm to another. A sequential policy based on a modified generalised likelihood ratio statistic is proposed. The policy, with a suitable threshold, is shown to satisfy the given constraint on the probability of false detection. Further, the proposed policy is asymptotically optimal in terms of the total cost among all policies that satisfy the constraint on the probability of false detection.