  Bayesian optimization (BO) has become a popular strategy for global
optimization of expensive real-world functions. Contrary to a common
expectation that BO is suited to optimizing black-box functions, it actually
requires domain knowledge about those functions to deploy BO successfully. Such
domain knowledge often manifests in Gaussian process (GP) priors that specify
initial beliefs on functions. However, even with expert knowledge, it is
non-trivial to quantitatively define a prior. This is especially true for
hyperparameter tuning problems on complex machine learning models, where
landscapes of tuning objectives are often difficult to comprehend. We seek an
alternative practice for setting these functional priors. In particular, we
consider the scenario where we have data from similar functions that allow us
to pre-train a tighter distribution a priori. We detail what pre-training
entails for GPs using a KL divergence based loss function, and propose a new
pre-training based BO framework named HyperBO. Theoretically, we show bounded
posterior predictions and near-zero regrets for HyperBO without assuming the
"ground truth" GP prior is known. To verify our approach in realistic setups,
we collect a large multi-task hyperparameter tuning dataset by training tens of
thousands of configurations of near-state-of-the-art deep learning models on
popular image and text datasets, as well as a protein sequence dataset. Our
results show that on average, HyperBO is able to locate good hyperparameters at
least 3 times more efficiently than the best competing methods on both our new
tuning dataset and existing multi-task BO benchmarks.
