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视为贝叶斯优化算法的致命弱点。受维数灾难的推动，大量算法旨在通过通常对目标函数施加各种简化假设来提高其在此类场景中的性能。本文识别了导致标准贝叶斯优化在高维任务中表现不佳的退化问题，并进一步展示了现有算法如何通过降低模型复杂度的视角来应对这些退化问题。此外，我们针对标准贝叶斯优化算法中常见的先验假设提出了一项增强方案，该方案在不强加目标结构限制的情况下将复杂度降至可控水平。我们的改进——即高斯过程长度尺度的先验随维度进行简单缩放——表明标准贝叶斯优化在高维空间中表现远超此前认知，在多个常见真实世界高维任务中明显优于现有最先进算法。