Efficient Learning for Selecting Top-m Context-Dependent Designs

We consider a simulation optimization problem for context-dependent decision-making, which aims to determine the top- <tex-math notation="LaTeX">m</tex-math> 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 probability of false selection. The proposed sampling policy is proved to be consistent, and its asymptotic sampling ratios are shown to be asymptotically optimal. Numerical experiments demonstrate that the proposed method improves the efficiency for selecting top- <tex-math notation="LaTeX">m</tex-math> context-dependent designs. Note to Practitioners —The performance of a given design may vary across different contexts, and better decision-making is possible by refining the available contextual information. We consider a context-dependent ranking and selection problem, which allows optimal selection to depend on contextual information obtained prior to decision-making. We develop a dynamic sampling scheme to efficiently learn and select the top- <tex-math notation="LaTeX">m</tex-math> designs in all contexts. Numerical experiments, including a honeypot deception game problem and a medical resource allocation problem, demonstrate that the proposed sampling scheme significantly improves the efficiency of context-dependent ranking and selection for the top- <tex-math notation="LaTeX">m</tex-math> designs.