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.

翻译：贝叶斯优化（BO）是一种用于全局优化黑箱函数的方法。尽管BO已成功应用于众多场景，但开发能扩展到高维域函数的高效BO算法仍是一大挑战。使用原始BO优化此类函数极为耗时。基于将高维空间嵌入低维空间思想的高维BO替代策略，对需要预先指定的嵌入维度选择敏感。我们提出了一种新的基于变量选择的计算高效高维BO方法。该方法无需预设任何超参数，即可自动学习坐标对齐的子空间（即包含选定变量的空间）。我们从理论上分析了算法的计算复杂度并推导了遗憾界。通过多个合成问题与实际问题上的实验，我们经验性地验证了所提方法的有效性。