Semi-supervised Embedding Learning for High-dimensional Bayesian Optimization

Bayesian optimization is a broadly applied methodology to optimize the expensive blackbox function. Despite its success, it still faces the challenge from the high-dimensional search space. To alleviate this problem, we propose a novel Bayesian optimization framework, which finds a low-dimensional space to perform Bayesian optimization through a semi-supervised, iterative, and embedding learning-based method (SILBO). SILBO incorporates both labeled and unlabeled points acquired from the acquisition function of Bayesian optimization to guide the learning of embedding space. To accelerate the learning procedure, we present a randomized method for generating the projection matrix. Furthermore, to map from the low-dimensional space to the high-dimensional original space, we propose two mapping strategies: SILBO-BU and SILBO-TD according to the evaluation overhead of the objective function. Experimental results on both synthetic function and hyperparameter optimization tasks demonstrate that SILBO outperforms the existing state-of-the-art high-dimensional Bayesian optimization methods.