  We consider sequential decision problems in which we adaptively choose one of
finitely many alternatives and observe a stochastic reward. We offer a new
perspective of interpreting Bayesian ranking and selection problems as adaptive
stochastic multi-set maximization problems and derive the first finite-time
bound of the knowledge-gradient policy for adaptive submodular objective
functions. In addition, we introduce the concept of prior-optimality and
provide another insight into the performance of the knowledge gradient policy
based on the submodular assumption on the value of information. We demonstrate
submodularity for the two-alternative case and provide other conditions for
more general problems, bringing out the issue and importance of submodularity
in learning problems. Empirical experiments are conducted to further illustrate
the finite time behavior of the knowledge gradient policy.
