Adaptive Sensing Resource Allocation Over Multiple Hypothesis Tests

This paper considers multiple binary hypothesis tests with adaptive allocation of sensing resources from a shared budget over a small number of stages. A Bayesian formulation is provided for the multistage allocation problem of minimizing the sum of Bayes risks, which is then recast as a dynamic program. In the single-stage case, the problem is a non-convex optimization, for which an algorithm composed of a series of parallel one-dimensional minimizations is presented. This algorithm ensures a global minimum under a sufficient condition. In the multistage case, the approximate dynamic programming method of open-loop feedback control is employed. In numerical simulations, the proposed allocation policies outperform alternative adaptive procedures when the numbers of true null and alternative hypotheses are not too imbalanced. In the case of few alternative hypotheses, the proposed policies are competitive using only a few stages of adaptation. In all cases substantial gains over non-adaptive sensing are observed.