  This work investigates the sequential hypothesis testing problem with online
sensor selection and sensor usage constraints. That is, in a sensor network,
the fusion center sequentially acquires samples by selecting one "most
informative" sensor at each time until a reliable decision can be made. In
particular, the sensor selection is carried out in the online fashion since it
depends on all the previous samples at each time. Our goal is to develop the
sequential test (i.e., stopping rule and decision function) and sensor
selection strategy that minimize the expected sample size subject to the
constraints on the error probabilities and sensor usages. To this end, we first
recast the usage-constrained formulation into a Bayesian optimal stopping
problem with different sampling costs for the usage-contrained sensors. The
Bayesian problem is then studied under both finite- and infinite-horizon
setups, based on which, the optimal solution to the original usage-constrained
problem can be readily established. Moreover, by capitalizing on the structures
of the optimal solution, a lower bound is obtained for the optimal expected
sample size. In addition, we also propose algorithms to approximately evaluate
the parameters in the optimal sequential test so that the sensor usage and
error probability constraints are satisfied. Finally, numerical experiments are
provided to illustrate the theoretical findings, and compare with the existing
methods.
