https://hal.inria.fr/hal-03124928Lyu, XiongXiongLyuUC Santa Barbara - University of California [Santa Barbara] - UC - University of CaliforniaBinois, MickaelMickaelBinoisACUMES - Analysis and Control of Unsteady Models for Engineering Sciences - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en AutomatiqueLudkovski, MichaelMichaelLudkovskiUC Santa Barbara - University of California [Santa Barbara] - UC - University of CaliforniaEvaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set EstimationHAL CCSD2021[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Binois, Mickaël2021-01-29 10:07:562023-03-15 08:58:092021-01-29 10:07:56enJournal articles10.1007/s11222-021-10014-w1We 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. 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 of Bermudan options in finance.