Adaptive Adversarial Multi-Armed Bandit Approach to Two-Person Zero-Sum Markov Games

Abstract

This technical note presents a recursive sampling-based algorithm for finite horizon two-person zero-sum Markov games (MGs) based on the Exp3 algorithm developed by Auer et al <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</i> for adaptive adversarial multi-armed bandit problems. We provide a finite-iteration bound to the equilibrium value of the induced ¿sample average approximation game¿ of a given MG and prove asymptotic convergence to the equilibrium value of the given MG. The time and space complexities of the algorithm are independent of the state space of the game.