Parallel Bayesian Global Optimization of Expensive Functions

• 成果类型: Article
• 署名作者: Wang, Jialei; Clark, Scott C.; Liu, Eric; Frazier, Peter, I
• 署名单位: Cornell University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2019.1966
• 发表日期: 2020
• 页码: 1850-1865
• 关键词: performance; simulation

摘要

We consider parallel global optimization of derivative-free expensive-to-evaluate functions, and propose an efficient method based on stochastic approximation for implementing a conceptual Bayesian optimization algorithm proposed by Ginsbourger in 2008. At the heart of this algorithm is maximizing the information criterion called the multipoints expected improvement, or the q-EI. To accomplish this, we use infinitesimal perturbation analysis (IPA) to construct a stochastic gradient estimator and show that this estimator is unbiased. We also show that the stochastic gradient ascent algorithm using the constructed gradient estimator converges to a stationary point of the q-EI surface, and therefore, as the number of multiple starts of the gradient ascent algorithm and the number of steps for each start grow large, the one-step Bayes-optimal set of points is recovered. We show in numerical experiments using up to 128 parallel evaluations that our method for maximizing the q-EI is faster than methods based on closed-form evaluation using high-dimensional integration, when considering many parallel function evaluations, and is comparable in speed when considering few. We also show that the resulting one-step Bayes-optimal algorithm for parallel global optimization finds high-quality solutions with fewer evaluations than a heuristic based on approximately maximizing the q-EI. A high-quality open source implementation of this algorithm is available in the open source Metrics Optimization Engine (MOE).