Black-box problems are common in real life like structural design, drug experiments, and machine learning. When optimizing black-box systems, decision-makers always consider multiple performances and give the final decision by comprehensive evaluations. Motivated by such practical needs, we focus on constrained black-box problems where the objective and constraints lack known special structure, and evaluations are expensive and even with noise. We develop a novel constrained Bayesian optimization approach based on the knowledge gradient method ($c-\rm{KG}$). A new acquisition function is proposed to determine the next batch of samples considering optimality and feasibility. An unbiased estimator of the gradient of the new acquisition function is derived to implement the $c-\rm{KG}$ approach.
翻译:黑箱问题在现实生活中是常见的,比如结构设计、药物实验和机器学习。当优化黑箱系统时,决策者总是会考虑多种表现,并通过全面评价作出最后决定。受这种实际需要的驱动,我们把重点放在目标与限制缺乏已知的特殊结构、评估费用昂贵甚至噪音等有限的黑箱问题。我们根据知识梯度方法(c-rm{KG}$)开发了一种新的限制贝叶斯优化方法。我们提出了一个新的获取功能,以确定下一批样本,以考虑最佳性和可行性。一个新的获取功能的梯度的公正估测员将用来实施$-rm{K}$的方法。