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Recursive Estimation of a Failure Probability for a Lipschitz Function

Abstract : Let g : Ω = [0, 1] d → R denote a Lipschitz function that can be evaluated at each point, but at the price of a heavy computational time. Let X stand for a random variable with values in Ω such that one is able to simulate, at least approximately, according to the restriction of the law of X to any subset of Ω. For example, thanks to Markov chain Monte Carlo techniques, this is always possible when X admits a density that is known up to a normalizing constant. In this context, given a deterministic threshold T such that the failure probability p := P(g(X) > T) may be very low, our goal is to estimate the latter with a minimal number of calls to g. In this aim, building on Cohen et al. [9], we propose a recursive and optimal algorithm that selects on the fly areas of interest and estimate their respective probabilities.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03301765
Contributor : Arnaud Guyader <>
Submitted on : Wednesday, July 28, 2021 - 2:40:47 PM
Last modification on : Friday, July 30, 2021 - 3:21:00 AM

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  • HAL Id : hal-03301765, version 1
  • ARXIV : 2107.13369

Citation

Lucie Bernard, Albert Cohen, Arnaud Guyader, Florent Malrieu. Recursive Estimation of a Failure Probability for a Lipschitz Function. 2021. ⟨hal-03301765⟩

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