High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces

TL;DR

This paper introduces SAASBO, a high-dimensional Bayesian optimization method that efficiently identifies sparse subspaces using Hamiltonian Monte Carlo, improving sample efficiency without requiring problem-specific hyperparameters.

Contribution

The paper proposes a novel BO approach leveraging Gaussian processes on sparse axis-aligned subspaces with HMC inference, enhancing high-dimensional optimization performance.

Findings

SAASBO outperforms existing methods on synthetic problems.

It achieves competitive results on real-world tasks.

No need for problem-specific hyperparameter tuning.

Abstract

Bayesian optimization (BO) is a powerful paradigm for efficient optimization of black-box objective functions. High-dimensional BO presents a particular challenge, in part because the curse of dimensionality makes it difficult to define -- as well as do inference over -- a suitable class of surrogate models. We argue that Gaussian process surrogate models defined on sparse axis-aligned subspaces offer an attractive compromise between flexibility and parsimony. We demonstrate that our approach, which relies on Hamiltonian Monte Carlo for inference, can rapidly identify sparse subspaces relevant to modeling the unknown objective function, enabling sample-efficient high-dimensional BO. In an extensive suite of experiments comparing to existing methods for high-dimensional BO we demonstrate that our algorithm, Sparse Axis-Aligned Subspace BO (SAASBO), achieves excellent performance on several synthetic and real-world problems without the need to set problem-specific hyperparameters.