Actively Learning Joint Contours of Multiple Computer Experiments

Contour location---the process of sequentially training a surrogate model to identify the design inputs that result in a pre-specified response value from a single computer experiment---is a well-studied active learning problem. Here, we tackle a related but distinct problem: identifying the input configuration that returns pre-specified values of multiple computer experiments simultaneously. Motivated by computer experiments of the rotational torques acting upon a vehicle in flight, we aim to identify stable flight conditions that result in zero torque forces. We propose a ``joint contour location'' (jCL) scheme that strikes a strategic balance between exploring the multiple response surfaces while exploiting learning of the intersecting contours. Rather than working exploration and exploitation into a single acquisition function, we devise two distinct acquisition schemes with a decision rule to choose between the two, which also provides a natural stopping criterion if no solution is present. We employ traditional Gaussian processes (GPs), multitask GPs, and deep GPs, but our jCL procedure is applicable to any surrogate that can provide posterior predictive distributions. Our jCL designs significantly outperform existing (single response) CL strategies, optimization-based alternatives, and previous strategies for targeting joint contours, enabling us to efficiently locate the optimal configurations for our motivating computer experiments.