  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.
