Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selection

• URL: http://arxiv.org/abs/2109.09264v2
• Date: Mon, 12 Feb 2024 17:22:28 GMT
• Title: Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selection
• Authors: Yihang Shen and Carl Kingsford
• Abstract summary: 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. We empirically show the efficacy of our method on several synthetic and real problems.
• Score: 0.5439020425818999
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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