Vanilla Bayesian Optimization Performs Great in High Dimensions
This addresses the long-standing challenge of scaling Bayesian optimization to high-dimensional problems, which is crucial for applications like hyperparameter tuning and experimental design, though it appears incremental as it modifies prior assumptions rather than introducing a new paradigm.
The paper tackles the problem of Bayesian optimization performing poorly in high dimensions by identifying degeneracies and proposing a simple scaling of the Gaussian process lengthscale prior with dimensionality. The result shows that this modification enables standard Bayesian optimization to clearly outperform existing state-of-the-art algorithms on multiple real-world high-dimensional tasks.
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.