Title: Ranking and Selection as Stochastic Control,
Abstract: Under a Bayesian framework, we formulate the fully sequential sampling and
selection decision in statistical ranking and selection as a stochastic control
problem, and derive the associated Bellman equation. Using value function
approximation, we derive an approximately optimal allocation policy. We show
that this policy is not only computationally efficient but also possesses both
one-step-ahead and asymptotic optimality for independent normal sampling
distributions. Moreover, the proposed allocation policy is easily generalizable
in the approximate dynamic programming paradigm.