Selecting the Optimal System Design under Covariates

In this research, we consider the ranking and selection problem in the presence of covariates. It is an important problem in personalized decision making. The performance of each design alternative depends on the values of the covariates to the simulation model for which the relationship is hard to describe analytically. Therefore the optimal design under each possible covariate value needs to be estimated by simulation. This work first introduces three measures to evaluate the selection quality over the covariate space and investigates their rate functions of convergence. By optimizing the rate functions, an asymptotically optimal budget allocation rule is developed and a corresponding selection algorithm is devised. We further show that the selection algorithm can recover the asymptotical optimal allocation in the limit. The high efficiency of the selection algorithm is illustrated via numerical testing.