Information utility in active sequential hypothesis testing

This paper considers a broad spectrum of applications in cognition, communications, design of experiments, and sensor management. In all of these applications, a decision maker is responsible to control the system dynamically so as to enhance his information in a speedy manner about an underlying phenomena of interest while accounting for the cost of communication, sensing, or data collection. In addition, due to the sequential nature of the problem, the decision maker relies on his current information state to constantly (re-)evaluate the information utility of various actions. In this paper, using a dynamic programming interpretation, an optimal notion of information utility is derived. Inspired by this view of the problem, a set of heuristic policies for dynamic selection of actions are proposed. The construction of these heuristics relate various notions of information utility with the statistical properties of the outcome, such as Kullback-Leibler divergence and mutual information. Via numerical and asymptotic analysis, the performance of these policies, hence the utility of the statistical quantities such as divergence and mutual information, in the context of the active hypothesis testing is investigated.