Title: Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation,
Abstract: We consider the problem of learning the level set for which a noisy black-box
function exceeds a given threshold.
To efficiently reconstruct the level set, we investigate Gaussian process
(GP) metamodels. Our focus is on strongly stochastic samplers, in particular
with heavy-tailed simulation noise and low signal-to-noise ratio.
To guard against noise misspecification, we assess the performance of three
variants: (i) GPs with Student-$t$ observations; (ii) Student-$t$ processes
(TPs); and (iii) classification GPs modeling the sign of the response. As a
fourth extension, we study GP surrogates with monotonicity constraints that are
relevant when the level set is known to be connected. In conjunction with these
metamodels, we analyze several acquisition functions for guiding the sequential
experimental designs, extending existing stepwise uncertainty reduction
criteria to the stochastic contour-finding context. This also motivates our
development of (approximate) updating formulas to efficiently compute such
acquisition functions. Our schemes are benchmarked by using a variety of
synthetic experiments in 1--6 dimensions. We also consider an application of
level set estimation for determining the optimal exercise policy and valuation
of Bermudan options in finance.