We consider stochastic approximation algorithms with constant step
size whose average ordinary differential equation (ODE) is cooperative and
irreducible. We show that, under mild conditions on the noise process,
invariant measures and empirical occupations measures of the process weakly
converge (as the time goes to infinity and the step size goes to zero) toward
measures which are supported by stable equilibria of the ODE. These results are
applied to analyzing the long-term behavior of a class of learning processes
arising in game theory.
Publié le : 1999-02-14
Classification:
Stochastic approximation,
ordinary differential equation method,
cooperative vector fields,
large deviations,
weak convergence,
theory of learning in games,
62L20,
34C35,
34F05,
93E35
@article{1029962603,
author = {Bena\"\i m, Michel and Hirsch, Morris W.},
title = {Stochastic approximation algorithms with constant step size whose
average is cooperative},
journal = {Ann. Appl. Probab.},
volume = {9},
number = {1},
year = {1999},
pages = { 216-241},
language = {en},
url = {http://dml.mathdoc.fr/item/1029962603}
}
Benaïm, Michel; Hirsch, Morris W. Stochastic approximation algorithms with constant step size whose
average is cooperative. Ann. Appl. Probab., Tome 9 (1999) no. 1, pp. 216-241. http://gdmltest.u-ga.fr/item/1029962603/