A Near - Optimal Polynomial TimeAlgorithm for Learning in StochasticGames

We present a new algorithm for polynomial time learning of optimal behavior in stochastic games. This algorithm incorporates and integrates important recent results of Kearns and Singh 5] in reinforcement learning and of Monderer and Tennenholtz 7] in repeated games. In stochastic games, the agent must cope with the existence of an adversary whose actions can be arbitrary. In particular, this adversary can withhold information about the game matrix by refraining from (or rarely) performing certain actions. This forces upon us an exploration vs. exploitation dilemma more complex than in Markov decision processes. Namely, given information about particular parts of a game matrix, how much eeort should the agent invest in learning its unknown parts. We explain and address these issues within the class of single controller stochastic games and explain how these ideas can be extended to stochastic games in general.