Recursive Estimation of a Failure Probability for a Lipschitz Function
The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 75-97.

Let g:Ω=[0,1] d 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:=(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 (in a certain sens) optimal algorithm that selects on the fly areas of interest and estimates their respective probabilities.

Published online:
DOI: 10.5802/smai-jcm.80
Classification: 60J20, 65C05, 65C05, 68Q25, 68W20
Keywords: Sequential design, Probability of failure, Sequential Monte Carlo, Tree based algorithms, High dimension

Lucie Bernard 1; Albert Cohen 2; Arnaud Guyader 3; Florent Malrieu 1

1 IDP, Université de Tours, France
2 LJLL, Sorbonne Université, France
3 LPSM, Sorbonne Université, France
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Lucie Bernard; Albert Cohen; Arnaud Guyader; Florent Malrieu. Recursive Estimation of a Failure Probability for a Lipschitz Function. The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 75-97. doi : 10.5802/smai-jcm.80. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.80/

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