Optimal computation budget allocation with Gaussian process regression

We consider Ranking and Selection (R&S) in the presence of spatial correlation among designs. The performance of each design can only be evaluated through stochastic simulation with heterogeneous noise. Our primary objective is to maximize the probability of correct selection (PCS) by optimally allocating the simulation budget considering the spatial correlation among designs. We propose using Gaussian process regression (GPR) to model the spatial correlation and develop a GPR-based optimal computing budget allocation (GPOCBA) framework to derive an asymptotically optimal allocation policy. Additionally, we analyze the impact of spatial correlation on allocation policy and quantify its benefits under specific cases. We also introduce a sequential implementation of GPOCBA and establish convergence results. Numerical experiments show that the proposed GPOCBA method significantly outperforms the widely used OCBA, demonstrating improved computational efficiency by considering spatial correlation in R&S problems.