策略形式博弈中常步长扰动学习自动机的随机稳定性分析
Stochastic Stability Analysis of Perturbed Learning Automata with Constant Step-Size in Strategic-Form Games
摘要：
本文考虑了学习自动机家族中的一类随机学习，并给出了策略型对策的随机稳定性分析。对于这类动态，收敛到纯纳什均衡已被证明只为罚款类潜在的游戏。先前的工作主要通过随机近似提供动态的收敛性质，其中渐近行为可以与常微分方程（ODE）的极限点相关联。然而，通过ODE近似分析全局收敛性需要存在一个李雅普诺夫或一个潜在的功能，这自然限制了这些算法的适用性，一类罚款的游戏。为了克服这些局限性，本文介绍了一种替代框架分析随机稳定性的基础上，明确表征的（唯一）不变的概率测度的诱导马尔可夫链。
英文摘要：
This paper considers a class of reinforcement-learning that belongs to the family of Learning Automata and provides a stochastic-stability analysis in strategic-form games. For this class of dynamics, convergence to pure Nash equilibria has been demonstrated only for the fine class of potential games. Prior work primarily provides convergence properties of the dynamics through stochastic approximations, where the asymptotic behavior can be associated with the limit points of an ordinary-differential equation (ODE). However, analyzing global convergence through the ODE-approximation requires the existence of a Lyapunov or a potential function, which naturally restricts the applicabity of these algorithms to a fine class of games. To overcome these limitations, this paper introduces an alternative framework for analyzing stochastic-stability that is based upon an explicit characterization of the (unique) invariant probability measure of the induced Markov chain.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
