Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selection
This addresses the problem of time-consuming optimization in high-dimensional domains for researchers and practitioners using BO, representing an incremental improvement over existing embedding-based methods.
The paper tackles the challenge of scaling Bayesian Optimization (BO) to high-dimensional functions by developing a method that uses variable selection to automatically learn axis-aligned sub-spaces without pre-specified hyperparameters, achieving computational efficiency as shown in empirical tests on synthetic and real problems.
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.