  Bayesian Optimization (BO) is a method for globally optimizing black-box
functions. While BO has been successfully applied to many scenarios, developing
effective BO algorithms that scale to functions with high-dimensional domains
is still a challenge. Optimizing such functions by vanilla BO is extremely
time-consuming. Alternative strategies for high-dimensional BO that are based
on the idea of embedding the high-dimensional space to the one with low
dimension are sensitive to the choice of the embedding dimension, which needs
to be pre-specified. We develop a new computationally efficient
high-dimensional BO method that exploits variable selection. Our method is able
to automatically learn axis-aligned sub-spaces, i.e. spaces containing selected
variables, without the demand of any pre-specified hyperparameters. We
theoretically analyze the computational complexity of our algorithm and derive
the regret bound. We empirically show the efficacy of our method on several
synthetic and real problems.
