  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.
