Online Appendix for 'Efficient Learning for Selecting Top-m Context-Dependent Designs'

Abstract

Online Appendix for "Efficient Learning for Selecting Top-m Context-Dependent Designs", which is submitted to the IEEE Transactions On Automation Science And Engineering. We consider a simulation optimization problem for a context-dependent decision-making, which aims to determine the top-m designs for all contexts. Under a Bayesian framework, we formulate the optimal dynamic sampling decision as a stochastic dynamic programming problem, and develop a sequential sampling policy to efficiently learn the performance of each design under each context. The asymptotically optimal sampling ratios are derived to attain the optimal large deviations rate of the worst-case of probability of false selection. The proposed sampling policy is proved to be consistent and its asymptotic sampling ratios are asymptotically optimal. Numerical experiments demonstrate that the proposed method improves the efficiency for selection of top-m context-dependent designs.

Keywords: Simulation optimization; context-dependent decision; top-m selection; dynamic sampling; asymptotic optimality.