We develop a simulation-based method for the online updating of Gaussian
process (GP) models by particle learning (PL) for regression and classification
problems. Our method exploits the sequential nature of PL inference to produce
a thrifty sequential design algorithm, in terms of computational speed,
compared to batch and other MCMC-based methods which must be re-started and
iterated to convergence with the inclusion of each new design point. We develop
the PL implementation of two active learning criteria commonly used with GPs
and MCMC: the expected improvement statistic for optimizing a noisy function,
and the predictive entropy for online exploration of classification boundaries.
We also demonstrate how the ensemble aspects of PL lead to a better exploration
of the posterior distribution compared to MCMC, which can suffer from mixing
problems.