  We introduce a method combining variational autoencoders (VAEs) and deep
metric learning to perform Bayesian optimisation (BO) over high-dimensional and
structured input spaces. By adapting ideas from deep metric learning, we use
label guidance from the blackbox function to structure the VAE latent space,
facilitating the Gaussian process fit and yielding improved BO performance.
Importantly for BO problem settings, our method operates in semi-supervised
regimes where only few labelled data points are available. We run experiments
on three real-world tasks, achieving state-of-the-art results on the penalised
logP molecule generation benchmark using just 3% of the labelled data required
by previous approaches. As a theoretical contribution, we present a proof of
vanishing regret for VAE BO.
