Title: Active Hypothesis Testing: Beyond Chernoff-Stein,
Abstract: An active hypothesis testing problem is formulated. In this problem, 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 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 this
problem, lower and upper bounds on the optimal misclassification probability
are derived and these bounds are shown to be asymptotically tight. In the
analysis, a sub-problem, which can be viewed as a generalization of the
Chernoff-Stein lemma, is formulated and analyzed. A heuristic approach to
strategy design is proposed and its relationship with existing heuristic
strategies is discussed.