Fixed-Horizon Active Hypothesis Testing

Abstract

Two active hypothesis testing problems are formulated. In these problems, the agent can perform a fixed number of experiments and then decide on one of the hypotheses or declare its experiments inconclusive. The first problem is an asymmetric formulation in which the objective is to minimize the probability of incorrectly declaring a particular hypothesis to be true while ensuring that the probability of correctly declaring that hypothesis is moderately high. This formulation is a generalization of the formulation in the Chernoff–Stein lemma to an active setting. The second problem is a symmetric formulation in which the objective is to minimize the misclassification probability while ensuring that the true hypothesis is declared conclusively with moderately high probability. For these problems, lower and upper bounds on the optimal misclassification probabilities are derived and these bounds are shown to be asymptotically tight. Novel experiment selection strategies are provided. It is shown that these strategies are asymptotically optimal and using numerical experiments, it is demonstrated that these strategies have a significantly better performance in the nonasymptotic regime.