Ranking and Selection as Stochastic Control
This work addresses the challenge of efficient decision-making in ranking and selection for researchers and practitioners in statistics and operations research, representing an incremental improvement through a novel method for a known bottleneck.
The authors tackled the problem of fully sequential sampling and selection in statistical ranking and selection by formulating it as a stochastic control problem under a Bayesian framework, deriving an approximately optimal allocation policy that is computationally efficient and possesses one-step-ahead and asymptotic optimality for independent normal sampling distributions.
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.