Upper-Confidence-Bound Procedure for Robust Selection of The Best

Robust selection of the best (RSB) is an important problem in the simulation area, when there exists input uncertainty in the underlying simulation model. RSB models this input uncertainty by a discrete ambiguity set and then proposes a two-layer framework under which the best alternative is defined to have the best worst-case mean performance over the ambiguity set. In this paper, we adopt a fixed-budget framework to address the RSB problem. Specifically, in contrast with existing procedures, we develop a new robust upper-confidence-bound (UCB) procedure, named as R-UCB. We can show that, the R-UCB procedure successfully inherits the simplicity and convergence guarantee of the traditional UCB procedure. Furthermore, simulation experiments demonstrate that the R-UCB procedure numerically outperforms the existing RSB procedures.