High-Dimensional Bayesian Optimization via Semi-Supervised Learning with Optimized Unlabeled Data Sampling

We introduce a novel semi-supervised learning approach, named Teacher-Student Bayesian Optimization ($\texttt{TSBO}$), integrating the teacher-student paradigm into BO to minimize expensive labeled data queries for the first time. $\texttt{TSBO}$ incorporates a teacher model, an unlabeled data sampler, and a student model. The student is trained on unlabeled data locations generated by the sampler, with pseudo labels predicted by the teacher. The interplay between these three components implements a unique *selective regularization* to the teacher in the form of student feedback. This scheme enables the teacher to predict high-quality pseudo labels, enhancing the generalization of the GP surrogate model in the search space. To fully exploit $\texttt{TSBO}$, we propose two optimized unlabeled data samplers to construct effective student feedback that well aligns with the objective of Bayesian optimization. Furthermore, we quantify and leverage the uncertainty of the teacher-student model for the provision of reliable feedback to the teacher in the presence of risky pseudo-label predictions. $\texttt{TSBO}$ demonstrates significantly improved sample-efficiency in several global optimization tasks under tight labeled data budgets. The implementation is available at https://github.com/reminiscenty/TSBO-Official.