Bayesian Optimization via Simulation with Pairwise Sampling and Correlated Prior Beliefs

Abstract

This paper addresses discrete optimization via simulation. We show that allowing for both a correlated prior distribution on the means (e.g., with discrete Kriging models) and sampling correlation (e.g., with common random numbers, or CRN) can significantly improve the ability to quickly identify the best alternative. These two correlations are brought together for the first time in a highly sequential knowledge-gradient sampling algorithm, which chooses points to sample using a Bayesian value of information (VOI) criterion. We provide almost sure convergence guarantees as the number of samples grows without bound when parameters are known and provide approximations that allow practical implementation including a novel use of the VOI’s gradient rather than the response surface’s gradient. We demonstrate that CRN leads to improved optimization performance for VOI-based algorithms in sequential sampling environments with a combinatorial number of alternatives and costly samples.