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We consider the problem of learning the level set for which a noisy black-boxfunction exceeds a given threshold. To efficiently reconstruct the level set,we investigate Gaussian process (GP) metamodels. Our focus is on stronglystochastic samplers, in particular with heavy-tailed simulation noise and lowsignal-to-noise ratio. To guard against noise misspecification, we assess theperformance of three variants: (i) GPs with Student-$t$ observations; (ii)Student-$t$ processes (TPs); and (iii) classification GPs modeling the sign ofthe response. In conjunction with these metamodels, we analyze severalacquisition functions for guiding the sequential experimental designs,extending existing stepwise uncertainty reduction criteria to the stochasticcontour-finding context. This also motivates our development of (approximate)updating formulas to efficiently compute such acquisition functions. Ourschemes are benchmarked by using a variety of synthetic experiments in 1--6dimensions. We also consider an application of level set estimation fordetermining the optimal exercise policy of Bermudan options in finance.

Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation