Bayesian optimization is an effective method for optimizing expensive-to-evaluate black-box functions. High-dimensional problems are particularly challenging as the surrogate model of the objective suffers from the curse of dimensionality, which makes accurate modeling difficult. We propose a group testing approach to identify active variables to facilitate efficient optimization in these domains. The proposed algorithm, Group Testing Bayesian Optimization (GTBO), first runs a testing phase where groups of variables are systematically selected and tested on whether they influence the objective. To that end, we extend the well-established theory of group testing to functions of continuous ranges. In the second phase, GTBO guides optimization by placing more importance on the active dimensions. By exploiting the axis-aligned subspace assumption, GTBO is competitive against state-of-the-art methods on several synthetic and real-world high-dimensional optimization tasks. Furthermore, GTBO aids in the discovery of active parameters in applications, thereby enhancing practitioners' understanding of the problem at hand.

翻译：贝叶斯优化是一种有效优化评估成本高昂的黑箱函数的方法。高维问题尤为棘手，因为目标函数的代理模型受维度灾难影响，导致精确建模困难。我们提出一种分组测试方法，通过识别活跃变量来促进这些领域的有效优化。所提出的算法——分组测试贝叶斯优化（GTBO）——首先运行一个测试阶段，系统性地选择变量组，并检验它们是否对目标函数有影响。为此，我们将成熟的分组测试理论扩展到连续值函数领域。在第二阶段，GTBO通过增加对活跃维度的重视来引导优化。通过利用坐标轴对齐子空间假设，GTBO在多个合成和真实世界的高维优化任务中与现有最优方法具有竞争力。此外，GTBO有助于发现应用中的活跃参数，从而加深实践者对问题的理解。