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.

翻译：贝叶斯优化是一种针对评估代价高昂或耗时的函数的优化框架。近期研究提出了函数网络的贝叶斯优化（BOFN），其中目标函数通过函数网络计算，每个函数以网络中前驱节点的输出和额外参数为输入。利用这种网络结构已被证明能显著提升性能。现有通用网络的BOFN算法需在每次迭代中评估完整网络，然而许多实际应用允许单独评估节点。为充分利用这一特性，我们提出一种用于BOFN的新型知识梯度采集函数，该函数可选择评估的节点及其输入，并具有成本感知能力。该方法通过以低于评估完整网络的成本评估部分网络，可大幅降低查询成本。我们提供了优化该采集函数的高效方案，并在多个合成与实际问题上证明其优于现有BOFN方法及其他基准。该采集函数是首个能对广义函数网络进行成本感知优化的方案。