Optimal search strategies in dynamic hypothesis testing

In this paper, we formulate and solve a class of dynamic search problems for obtaining the closed-loop sequence of measurements which optimally selects among many candidate hypotheses. We provide a sufficient condition for which the optimal strategy is characterized by a simple index rule which depends only on the ordering of the conditional probabilities of the hypotheses given the past measurements. We show that this index rule is optimal independent of the number of measurements to be taken. We also discuss counterexamples which illustrate that, when our conditions are relaxed, optimal policies are more complex. The results can be applied to solve optimally and efficiently complex problems in fault diagnosis and search with unreliable tests.