Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation
This work addresses level set estimation for stochastic samplers, which is incremental as it extends existing methods to handle noise misspecification and sequential designs.
The paper tackled the problem of learning level sets from noisy black-box functions, particularly with heavy-tailed noise and low signal-to-noise ratio, by evaluating Gaussian process metamodels and sequential designs, achieving performance benchmarks in synthetic experiments up to 6 dimensions and an application in finance for Bermudan options.
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. 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.