  Gaussian processes are the model of choice in Bayesian optimization and
active learning. Yet, they are highly dependent on cleverly chosen
hyperparameters to reach their full potential, and little effort is devoted to
finding good hyperparameters in the literature. We demonstrate the impact of
selecting good hyperparameters for GPs and present two acquisition functions
that explicitly prioritize hyperparameter learning. Statistical distance-based
Active Learning (SAL) considers the average disagreement between samples from
the posterior, as measured by a statistical distance. SAL outperforms the
state-of-the-art in Bayesian active learning on several test functions. We then
introduce Self-Correcting Bayesian Optimization (SCoreBO), which extends SAL to
perform Bayesian optimization and active learning simultaneously. SCoreBO
learns the model hyperparameters at improved rates compared to vanilla BO,
while outperforming the latest Bayesian optimization methods on traditional
benchmarks. Moreover, we demonstrate the importance of self-correction on
atypical Bayesian optimization tasks.
