Hedging Algorithms and Repeated Matrix Games

Playing repeated matrix games (RMG) while maximizing the cumulative returns is a basic method to evaluate multi-agent learning (MAL) algorithms. Previous work has shown that $UCB$, $M3$, $S$ or $Exp3$ algorithms have good behaviours on average in RMG. Besides, hedging algorithms have been shown to be effective on prediction problems. An hedging algorithm is made up with a top-level algorithm and a set of basic algorithms. To make its decision, an hedging algorithm uses its top-level algorithm to choose a basic algorithm, and the chosen algorithm makes the decision. This paper experimentally shows that well-selected hedging algorithms are better on average than all previous MAL algorithms on the task of playing RMG against various players. $S$ is a very good top-level algorithm, and $UCB$ and $M3$ are very good basic algorithms. Furthermore, two-level hedging algorithms are more effective than one-level hedging algorithms, and three levels are not better than two levels.