Bayesian Optimization via Simulation with Pairwise Sampling and Correlated Prior Beliefs

Jing Xie (), Peter I. Frazier () and Stephen E. Chick ()
Additional contact information
Jing Xie: Credibly, New York, New York 10010
Peter I. Frazier: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853
Stephen E. Chick: Technology and Operations Management Area, INSEAD, 77300 Fontainebleau, France

Operations Research, 2016, vol. 64, issue 2, 542-559

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.

Keywords: discrete optimization via simulation; value of information; Kriging; correlated samples (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (11)

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