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Probabilistic bisection with spatial metamodels

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  • Rodriguez, Sergio
  • Ludkovski, Michael

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.

Suggested Citation

  • Rodriguez, Sergio & Ludkovski, Michael, 2020. "Probabilistic bisection with spatial metamodels," European Journal of Operational Research, Elsevier, vol. 286(2), pages 588-603.
    • Handle: RePEc:eee:ejores:v:286:y:2020:i:2:p:588-603
    DOI: 10.1016/j.ejor.2020.03.049
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    References listed on IDEAS

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