Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selection

Bayesian Optimization (BO) is a widely-used method for the global optimization of black-box functions. While BO has been successfully applied to many scenarios, scaling BO algorithms to high-dimensional domains remains 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 leverages variable selection. We analyze the computational complexity of our algorithm and demonstrate its efficacy on several synthetic and real problems through empirical evaluations.