PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Finite time analysis of stratified sampling for monte carlo
Alexandra Carpentier and Rémi Munos
NIPS 2011 2011.


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 O(n−3/2) that depends on a measure of the disparity of the strata, and a distribution-free bound O(n-4/3) that does not.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
ID Code:8982
Deposited By:Rémi Munos
Deposited On:21 February 2012