Stochastic approximation algorithms with constant step size whose average is cooperative

• 成果类型: Article
• 署名作者: Benaïm, M; Hirsch, MW
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1999
• 页码: 216-241
• 关键词: differential-equations; urn processes; CONVERGENCE; systems; sets

摘要

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.