Efficient simulation budget allocation for contextual ranking and selection with quadratic models

This paper considers contextual ranking and selection problems where the objective is to identify the best design under every possible context. We assume the mean performance of each alternative design to be a quadratic function across a continuous context space. By judiciously pre-selecting a finite set of contexts for sampling and leveraging this quadratic model structure, we develop an efficient Bayesian budget allocation procedure that actively learns the problem instance and myopically improves decision quality across the context space. We prove the asymptotic consistency of our algorithm. We also conduct extensive numerical experiments using both synthetic functions and industrial examples whereby we show that our procedure can deliver significantly better performance against benchmark algorithms under both fixed-budget and fixed-precision settings.