Active M-ary sequential hypothesis testing

This paper considers a generalized sequential hypothesis testing problem in which a decision maker not only can sequentially trade off the sensing cost with the declaration precision, but also can exert control over the sensed information. Here, the decision maker´s action impacts the sensing cost as well as outcome. Numerically solving an appropriate DP, it is shown that the sensing outcome has a dual role: (1) it immediately reduces the uncertainty in the decision maker´s belief; and (2) it shapes the future belief via Bayes´ rule. This paper focuses on sufficient conditions rendering the optimal sensing actions independent of the current and future belief vector, and reducing the problem to a classical (passive) hypothesis testing problem.