  Bayesian optimization has been challenged by datasets with large-scale,
high-dimensional, and non-stationary characteristics, which are common in
real-world scenarios. Recent works attempt to handle such input by applying
neural networks ahead of the classical Gaussian process to learn a latent
representation. We show that even with proper network design, such learned
representation often leads to collision in the latent space: two points with
significantly different observations collide in the learned latent space,
leading to degraded optimization performance. To address this issue, we propose
LOCo, an efficient deep Bayesian optimization framework which employs a novel
regularizer to reduce the collision in the learned latent space and encourage
the mapping from the latent space to the objective value to be Lipschitz
continuous. LOCo takes in pairs of data points and penalizes those too close in
the latent space compared to their target space distance. We provide a rigorous
theoretical justification for LOCo by inspecting the regret of this
dynamic-embedding-based Bayesian optimization algorithm, where the neural
network is iteratively retrained with the regularizer. Our empirical results
demonstrate the effectiveness of LOCo on several synthetic and real-world
benchmark Bayesian optimization tasks.
