  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. The agent is also allowed to declare its experiments inconclusive
if needed. The first problem is an asymmetric formulation in which the 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 can be seen as a
generalization of the formulation in the classical Chernoff-Stein lemma to an
active setting. The second problem is a symmetric formulation in which the
objective is to minimize the probability of making an incorrect inference
(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. Classical
approaches for experiment selection suggest use of randomized and, in some
cases, open-loop strategies. As opposed to these classical approaches, fully
deterministic and adaptive experiment selection strategies are provided. It is
shown that these strategies are asymptotically optimal and further, using
numerical experiments, it is demonstrated that these novel experiment selection
strategies (coupled with appropriate inference strategies) have a significantly
better performance in the non-asymptotic regime.
