A class of non homogeneous self interacting random processes with applications to learning in games and vertex-reinforced random walks

TL;DR

This paper introduces a unified framework for analyzing non Markovian, non homogeneous stochastic processes, including models of reinforced random walks and learning in games, using set-valued dynamical systems.

Contribution

It develops a novel approximation method via set-valued dynamical systems for complex stochastic processes, enabling analysis of new models in reinforcement learning and game theory.

Findings

Unified approach to simulated annealing processes

New models of vertex reinforced random walks analyzed

Insights into learning dynamics in games including fictitious play

Abstract

Using an approximation by a set-valued dynamical system, this paper studies a class of non Markovian and non homogeneous stochastic processes on a finite state space. It provides an unified approach to simulated annealing type processes. It permits to study new models of vertex reinforced random walks and new models of learning in games including Markovian fictitious play.