Bayesian optimization is a framework for optimizing functions that are costly
or time-consuming to evaluate. Recent work has considered Bayesian optimization
of function networks (BOFN), where the objective function is computed via a
network of functions, each taking as input the output of previous nodes in the
network and additional parameters. Exploiting this network structure has been
shown to yield significant performance improvements. Existing BOFN algorithms
for general-purpose networks are required to evaluate the full network at each
iteration. However, many real-world applications allow evaluating nodes
individually. To take advantage of this opportunity, we propose a novel
knowledge gradient acquisition function for BOFN that chooses which node to
evaluate as well as the inputs for that node in a cost-aware fashion. This
approach can dramatically reduce query costs by allowing the evaluation of part
of the network at a lower cost relative to evaluating the entire network. We
provide an efficient approach to optimizing our acquisition function and show
it outperforms existing BOFN methods and other benchmarks across several
synthetic and real-world problems. Our acquisition function is the first to
enable cost-aware optimization of a broad class of function networks.

使用一种基于知识梯度获取函数关系网的新方法，使得节点评估和输入选择可以根据成本进行，从而降低了查询成本并在多个合成和真实问题中优于现有的函数网络方法和其他基准。