Finite time analysis of stratified sampling for monte carlo
Alexandra Carpentier and Rémi Munos
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.
|Project Keyword:||Project Keyword UNSPECIFIED|
|Deposited By:||Rémi Munos|
|Deposited On:||21 February 2012|