Active M-ary sequential hypothesis testing

Abstract

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.