Optimizing a black-box, expensive, and multi-extremal function, given multiple approximations, is a challenging task known as multi-information source optimization (MISO), where each source has a different cost and the level of approximation (aka fidelity) of each source can change over the search space. While most of the current approaches fuse the Gaussian processes (GPs) modelling each source, we propose to use GP sparsification to select only “reliable” function evaluations performed over all the sources. These selected evaluations are used to create an augmented Gaussian process (AGP), whose name is implied by the fact that the evaluations on the most expensive source are augmented with the reliable evaluations over less expensive sources. A new acquisition function, based on confidence bound, is also proposed, including both cost of the next source to query and the location-dependent approximation of that source. This approximation is estimated through a model discrepancy measure and the prediction uncertainty of the GPs. MISO-AGP and the MISO-fused GP counterpart are compared on two test problems and hyperparameter optimization of a machine learning classifier on a large dataset.

给定多个近似值，优化黑匣子，昂贵且具有多个极值的功能是一项艰巨的任务，称为多信息源优化（MISO），其中每个源的成本和近似度（即保真度）都不同。每个来源都可以在搜索空间中变化。尽管当前大多数方法融合了对每个源建模的高斯过程（GP），但我们建议使用GP稀疏化来选择仅对所有源执行的“可靠”功能评估。这些选定的评估用于创建增强的高斯过程（AGP），其名称隐含了以下事实：对最昂贵来源的评估得到了增强对较便宜的货源进行可靠的评估。还提出了一种基于置信区间的新采集功能，包括查询下一个数据源的成本以及该数据源的位置相关近似值。该近似值是通过模型差异度量和GP的预测不确定性来估计的。在两个测试问题和大型数据集上的机器学习分类器的超参数优化方面，对MISO-AGP和MISO融合的GP对应项进行了比较。