Kernel Learning for Sample Constrained Black-Box Optimization

Black box optimization (BBO) focuses on optimizing unknown functions in high-dimensional spaces. In many applications, sampling the unknown function is expensive, imposing a tight sample budget. Ongoing work is making progress on reducing the sample budget by learning the shape/structure of the function, known as kernel learning. We propose a new method to learn the kernel of a Gaussian Process. Our idea is to create a continuous kernel space in the latent space of a variational autoencoder, and run an auxiliary optimization to identify the best kernel. Results show that the proposed method, Kernel Optimized Blackbox Optimization ( KOBO), outperforms state of the art by estimating the optimal at considerably lower sample budgets. Results hold not only across synthetic benchmark functions but also in real applications. We show that a hearing aid may be personalized with fewer audio queries to the user, or a generative model could converge to desirable images from limited user ratings.