Joint Optimization and Variable Selection of High-dimensional Gaussian Processes

Understand

Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications.

• In this paper, we tackle this challenge by modeling the unknown function as a sample from a high-dimensional Gaussian process (GP) distribution.
• Assuming that the unknown function only depends on few relevant variables, we show that it is possible to perform joint variable selection and GP optimization.
• We provide strong performance guarantees for our algorithm, bounding the sample complexity of variable selection, and as well as providing cumulative regret bounds.