A Hierarchical Expected Improvement Method for Bayesian Optimization
针对传统期望改进方法过于贪婪、易陷入次优解的问题，提出分层期望改进框架，利用分层高斯过程模型鼓励探索，并证明全局收敛性，在合成函数和半导体制造优化中表现更优。
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. Supplementary materials for this article are available online.