Bayesian Optimization (BO) is a method for globally optimizing black-box func- tions. 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 one with low dimensions 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 analyze the computational complexity of our algorithm. We empirically show the efficacy of our method on several synthetic and real problems.