Sequential Sampling for a Ranking and Selection Problem with Exponential Sampling Distributions

We study a ranking and selection problem with exponential sampling distributions. Under a Bayesian framework, we derive the posterior distribution of the performance parameter, and provide a normal approximation for the posterior distribution based on a central limit theorem to efficiently learn about the performance parameter. We formulate dynamic sampling decision as a stochastic control problem, and propose a sequential sampling procedure, which maximizes a value function approximation one-step ahead and is proved to be consistent. Numerical results demonstrate the efficiency of the proposed method.