Extrinsic Jensen-Shannon divergence with application in active hypothesis testing

Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest while accounting for the penalty of wrong declarations. In this paper, Extrinsic Jensen-Shannon (EJS) divergence is introduced as a measure of information. Using EJS as an information utility, a heuristic policy for selecting actions is proposed. Via numerical and asymptotic optimality analysis, the performance of the proposed policy, hence the applicability of the EJS divergence in the context of the active hypothesis testing is investigated.