High-dimensional problems have long been considered the Achilles' heel of Bayesian optimization algorithms. Spurred by the curse of dimensionality, a large collection of algorithms aim to make it more performant in this setting, commonly by imposing various simplifying assumptions on the objective. In this paper, we identify the degeneracies that make vanilla Bayesian optimization poorly suited to high-dimensional tasks, and further show how existing algorithms address these degeneracies through the lens of lowering the model complexity. Moreover, we propose an enhancement to the prior assumptions that are typical to vanilla Bayesian optimization algorithms, which reduces the complexity to manageable levels without imposing structural restrictions on the objective. Our modification - a simple scaling of the Gaussian process lengthscale prior with the dimensionality - reveals that standard Bayesian optimization works drastically better than previously thought in high dimensions, clearly outperforming existing state-of-the-art algorithms on multiple commonly considered real-world high-dimensional tasks.

翻译：高维问题长期以来被认为是贝叶斯优化算法的致命弱点。受维数灾难的驱使，大量算法旨在通过施加各种简化假设来提高其在此场景中的性能。本文首先揭示了使香草贝叶斯优化难以胜任高维任务的退化机制，进而通过降低模型复杂度的视角，阐述了现有算法如何应对这些退化问题。此外，我们提出对香草贝叶斯优化算法典型先验假设的增强方案，该方案无需对目标函数施加结构限制即可将复杂度降至可管理水平。我们的改进——通过将高斯过程长度尺度先验与维数进行简单缩放——表明标准贝叶斯优化在高维空间中的性能远超先前认知，在多个常用真实世界高维任务中显著优于现有最先进算法。