Natural Sciences, Computer and Information Sciences, Computer graphics and computer vision, Naturvetenskap, Data- och informationsvetenskap (Datateknik), Datorgrafik och datorseende, Mathematical Sciences, Computational Mathematics, Matematik, Beräkningsmatematik

High-dimensional problems have long been considered the Achilles' heel of Bayesian optimization. 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, 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.