Adaptive Stratified Sampling for Monte-Carlo integration of Differentiable functions

A. Carpentier 1 R. Munos 1
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where the function oscillates more, while allocating the samples such that they are well spread on the domain (this notion shares similitude with low discrepancy). We prove that the estimate returned by the algorithm is almost similarly accurate as the estimate that an optimal oracle strategy (that would know the variations of the function \textiteverywhere) would return, and provide a finite-sample analysis.
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https://hal.inria.fr/hal-00943123
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Submitted on : Friday, February 7, 2014 - 8:23:59 AM
Last modification on : Thursday, February 21, 2019 - 10:52:49 AM

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A. Carpentier, R. Munos. Adaptive Stratified Sampling for Monte-Carlo integration of Differentiable functions. Advances in Neural Information Processing Systems, 2012, Lake Tahoe, United States. ⟨hal-00943123⟩

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