  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.
