The use of uniform sequences with low discrepancy instead of random sequences in expectations computings is known to improve the rate of convergence. We propose and justify their use for the BOBBINS-MONRO algorithm. To this end we introduce the concepts of averaging and strong averaging systems and then we give under somewhat more re¬strictive assumptions than in the random case a convergence theorem and an estimation of the rate of convergence which show their superiority to random sequences.
Publié le : 1990-01-04
Classification:
stochastic algorithm,
sequence with low discrepancy,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-01667083,
author = {Lapeyre, Bernard and Pages, Gilles and Sab, Karam},
title = {Sequences with low discrepancy generalisation and application to Robbins-Monro algorithm},
journal = {HAL},
volume = {1990},
number = {0},
year = {1990},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01667083}
}
Lapeyre, Bernard; Pages, Gilles; Sab, Karam. Sequences with low discrepancy generalisation and application to Robbins-Monro algorithm. HAL, Tome 1990 (1990) no. 0, . http://gdmltest.u-ga.fr/item/hal-01667083/