Ranking and Selection as Stochastic Control

• Published in: IEEE transactions on automatic control Vol. 63; no. 8; pp. 2359 - 2373
• Main Authors: Peng, Yijie, Chong, Edwin K. P., Chen, Chun-Hung, Fu, Michael C.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-08-2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation algorithms; Bayes methods; Bayesian; Bayesian analysis; Dynamic programming; dynamic sampling and selection; Function approximation; Mathematical model; Optimal control; Optimization; Ranking; Ranking (statistics); ranking and selection (R&S); Resource management; Sequential sampling; simulation; stochastic control; Stochastic processes
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2018.2797188

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 a 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.