Joint Optimization and Variable Selection of High-dimensional Gaussian   Processes
  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. We further provide empirical evidence on the effectiveness of our algorithm on several benchmark optimization problems. 
Bo Chen (Caltech), Rui Castro (Eindhoven University of Technology),   Andreas Krause (ETH Zurich)
cs.LG stat.ML