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Optimizing a black-box, expensive, and multi-extremal function, given multiple approximations, is a challenging task known as multi-information source optimization (MISO), where each source has a different cost and the level of approximation (aka  fidelity ) of each source can change over the search space. While most of the current approaches  fuse  the Gaussian processes (GPs) modelling each source, we propose to use GP  sparsification  to select only “reliable” function evaluations performed over all the sources. These selected evaluations are used to create an augmented Gaussian process (AGP), whose name is implied by the fact that the evaluations on the most expensive source are  augmented  with the reliable evaluations over less expensive sources. A new acquisition function, based on confidence bound, is also proposed, including both cost of the next source to query and the location-dependent approximation of that source. This approximation is estimated through a  model discrepancy  measure and the prediction uncertainty of the GPs. MISO-AGP and the MISO-fused GP counterpart are compared on two test problems and hyperparameter optimization of a machine learning classifier on a large dataset.

Sparsifying to optimize over multiple information sources: an augmented Gaussian process based algorithm