High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces
This work addresses the problem of sample-efficient optimization in high-dimensional black-box functions for researchers and practitioners in machine learning, representing an incremental improvement over existing methods.
The paper tackles the challenge of high-dimensional Bayesian optimization by proposing Gaussian process surrogate models on sparse axis-aligned subspaces, demonstrating that their SAASBO algorithm achieves excellent performance in experiments without requiring problem-specific hyperparameters.
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.