A Hierarchical Expected Improvement Method for Bayesian Optimization

• 成果类型: Article
• 署名作者: Chen, Zhehui; Mak, Simon; Wu, C. F. Jeff
• 署名单位: University System of Georgia; Georgia Institute of Technology; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2210803
• 发表日期: 2024
• 页码: 1619-1632
• 关键词: EFFICIENT GLOBAL OPTIMIZATION; knowledge-gradient; parameters; dimension; designs

摘要

The Expected Improvement (EI) method, proposed by Jones, Schonlau, andWelch, is a widely used Bayesian optimization method, which makes use of a fitted Gaussian process model for efficient black-box optimization. However, one key drawback of EI is that it is overly greedy in exploiting the fitted Gaussian process model for optimization, which results in suboptimal solutions even with large sample sizes. To address this, we propose a new hierarchical EI (HEI) framework, which makes use of a hierarchical Gaussian process model. HEI preserves a closed-form acquisition function, and corrects the over-greediness of EI by encouraging exploration of the optimization space. We then introduce hyperparameter estimation methods which allow HEI to mimic a fully Bayesian optimization procedure, while avoiding expensive Markov-chain Monte Carlo sampling steps. We prove the global convergence of HEI over a broad function space, and establish near-minimax convergence rates under certain prior specifications. Numerical experiments show the improvement of HEI over existing Bayesian optimization methods, for synthetic functions and a semiconductor manufacturing optimization problem. for this article are available online.