Fixed Confidence Ranking and Selection Under Input Uncertainty

In stochastic simulation, input uncertainty (IU) is caused by the error in estimating input distributions using finite real-world data. When it comes to simulation-based Ranking and Selection (R&S), ignoring IU can lead to the failure of many existing procedures. In this paper, we study a new version of the fixed confidence R&S problem, where sequential input data can be acquired to reduce IU over time. To solve the problem, we first propose a moving average estimator for online estimation with sequential data. Then, a new procedure is designed by extending a Sequential Elimination framework. As is shown numerically, our procedure can effectively achieve the desired probability of correct selection, but there is plenty of room for improving its efficiency.