Eecient Algorithms for Learning to Play Repeated Games against Computationally Bounded Adversaries

We study the problem of eeciently learning to play a game optimally against an unknown adversary chosen from a computationally bounded class. We both contribute to the line of research on playing games against nite automata, and expand the scope of this research by considering new classes of adversaries. We introduce the natural notions of games against recent history adversaries (whose current action is determined by some simple boolean formula on the recent history of play), and games against statistical adversaries (whose current action is determined by some simple function of the statistics of the entire history of play). In both cases we give eecient algorithms for learning to play penny-matching and a more diicult game called contract. We also give the most powerful positive result to date for learning to play against nite automata, an eecient algorithm for learning to play any game against any nite automata with probabilistic actions and low cover time.