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.

高维问题一直被认为是贝叶斯优化算法的致命软肋。本文通过识别导致标准贝叶斯优化在高维任务中性能不佳的退化情况，并通过减少模型复杂性的角度探究现有算法如何应对这些退化情况。此外，我们提出了一种增强对标准贝叶斯优化算法中先验假设的修改方法，通过与维度进行简单缩放的高斯过程长度尺度先验，揭示了在高维情况下标准贝叶斯优化比以往认为的表现要好得多，明显优于多个常见的真实高维任务的现有最先进算法。

高维空间中普通贝叶斯优化表现出色