Particle Learning of Gaussian Process Models for Sequential Design and Optimization

We develop a simulation-based method for the online updating of Gaussian process regression and classification models. Our method exploits sequential Monte Carlo to produce a fast sequential design algorithm for these models relative to the established MCMC alternative. The latter is less ideal for sequential design since it must be restarted and iterated to convergence with the inclusion of each new design point. We illustrate some attractive ensemble aspects of our SMC approach, and show how active learning heuristics may be implemented via particles to optimize a noisy function or to explore classification boundaries online. Supplemental material, including an R package, is available online.