Probabilistic bisection with spatial metamodels

Sergio Rodriguez and Michael Ludkovski

European Journal of Operational Research, 2020, vol. 286, issue 2, 588-603

Abstract: Probabilistic Bisection Algorithms perform root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and location-dependent, so that model inference and Bayesian knowledge updating must be performed simultaneously. To this end, we propose to leverage the spatial structure of a typical oracle by constructing a statistical surrogate for the underlying logistic regression step. We investigate several surrogates, including Binomial Gaussian Processes (B-GP), Polynomial, Kernel, and Spline Logistic Regression. In parallel, we develop sampling policies that adaptively balance learning the oracle distribution and learning the root. One of our proposals mimics active learning with B-GPs and provides a novel look-ahead predictive variance formula. The resulting gains of our Spatial PBA algorithm relative to earlier G-PBA models are illustrated with synthetic examples and a challenging stochastic root finding problem from Bermudan option pricing.

Keywords: Simulation; Stochastic root-finding; Simulation metamodeling; Uncertainty quantification (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:286:y:2020:i:2:p:588-603

DOI: 10.1016/j.ejor.2020.03.049

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