Finite-Time Analysis of Stratified Sampling for Monte Carlo

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 stratified sampling for Monte-Carlo integration. We model this problem in a multi-armed bandit setting, where the arms represent the strata, and the goal is to estimate a weighted average of the mean values of the arms. We propose a strategy that samples the arms according to an upper bound on their standard deviations and compare its estimation quality to an ideal allocation that would know the standard deviations of the strata. We provide two regret analyses: a distribution-dependent bound $\widetilde O(n^{-3/2})$ that depends on a measure of the disparity of the strata, and a distribution-free bound $\widetilde O(n^{-4/3})$ that does not.
Type de document :
Communication dans un congrès
NIPS - Twenty-Fifth Annual Conference on Neural Information Processing Systems, Dec 2011, Grenade, Spain. 2011
Domaine :

Littérature citée [15 références]

https://hal.inria.fr/inria-00636924
Contributeur : Alexandra Carpentier <>
Soumis le : lundi 27 février 2012 - 17:46:09
Dernière modification le : jeudi 11 janvier 2018 - 06:22:13
Document(s) archivé(s) le : jeudi 14 juin 2012 - 17:00:24

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• HAL Id : inria-00636924, version 3

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Alexandra Carpentier, Rémi Munos. Finite-Time Analysis of Stratified Sampling for Monte Carlo. NIPS - Twenty-Fifth Annual Conference on Neural Information Processing Systems, Dec 2011, Grenade, Spain. 2011. 〈inria-00636924v3〉

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