Bayesian optimization (BO) is a powerful tool for seeking the global optimum of black-box functions. While evaluations of the black-box functions can be highly costly, it is desirable to reduce the use of expensive labeled data. For the first time, we introduce a teacher-student model to exploit semi-supervised learning that can make use of large amounts of unlabelled data under the context of BO. Importantly, we show that the selection of the validation and unlabeled data is key to the performance of BO. To optimize the sampling of unlabeled data, we employ a black-box parameterized sampling distribution optimized as part of the employed bi-level optimization framework. Taking one step further, we demonstrate that the performance of BO can be further improved by selecting unlabeled data from a dynamically fitted extreme value distribution. Our BO method operates in a learned latent space with reduced dimensionality, making it scalable to high-dimensional problems. The proposed approach outperforms significantly the existing BO methods on several synthetic and real-world optimization tasks.

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