Title :
Adaptive Adversarial Multi-Armed Bandit Approach to Two-Person Zero-Sum Markov Games
Author :
Chang, Hyeong Soo ; Hu, Jiaqiao ; Fu, Michael C. ; Marcus, Steven I.
Author_Institution :
Dept. of Comput. Sci. & Eng., Sogang Univ., Seoul, South Korea
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. 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.
Keywords :
Markov processes; approximation theory; computational complexity; convergence; game theory; iterative methods; Exp3 algorithm; adaptive adversarial multiarmed bandit approach; asymptotic convergence; equilibrium value; finite horizon two-person zero-sum Markov games; finite-iteration bound; induced sample average approximation game; recursive sampling-based algorithm; space complexity; state space; time complexity; Approximation algorithms; Computer science; Convergence; Mathematics; Probability distribution; Sampling methods; State-space methods; Statistics; Multi-armed bandit; sample average approximation; sampling; two-person zero-sum Markov game (MG);
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2009.2036333
