A CLASS OF SELF-INTERACTING PROCESSES WITH APPLICATIONS TO GAMES AND REINFORCED RANDOM WALKS

被引：5

作者：

Benaim, Michel ^{[1
]}

Raimond, Olivier ^{[2
]}

机构：

[1] Univ Neuchatel, Inst Math, CH-2007 Neuchatel, Switzerland

[2] Univ Paris Ouest Nanterre La Defense, Dept Math, F-92000 Nanterre, France

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2010年 / 48卷 / 07期

基金：

瑞士国家科学基金会;

关键词：

stochastic approximation; processes with reinforcement; differential inclusions; learning in games; simulated annealing; STOCHASTIC APPROXIMATIONS; FICTITIOUS PLAY; CONVERGENCE;

D O I：

10.1137/080721091

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper studies a class of non-Markovian and nonhomogeneous stochastic processes on a finite state space. Relying on a recent paper by Benaim, Hofbauer, and Sorin [SIAM J. Control Optim., 44 (2005), pp. 328-348] it is shown that, under certain assumptions, the asymptotic behavior of occupation measures can be described in terms of a certain set-valued deterministic dynamical system. This provides a unified approach to simulated annealing type processes and permits the study of new models of vertex reinforced random walks and new models of learning in games such as Markovian fictitious play.

引用

页码：4707 / 4730

页数：24

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