  Active learning of Gaussian process (GP) surrogates has been useful for
optimizing experimental designs for physical/computer simulation experiments,
and for steering data acquisition schemes in machine learning. In this paper,
we develop a method for active learning of piecewise, Jump GP surrogates. Jump
GPs are continuous within, but discontinuous across, regions of a design space,
as required for applications spanning autonomous materials design,
configuration of smart factory systems, and many others. Although our active
learning heuristics are appropriated from strategies originally designed for
ordinary GPs, we demonstrate that additionally accounting for model bias, as
opposed to the usual model uncertainty, is essential in the Jump GP context.
Toward that end, we develop an estimator for bias and variance of Jump GP
models. Illustrations, and evidence of the advantage of our proposed methods,
are provided on a suite of synthetic benchmarks, and real-simulation
experiments of varying complexity.
