Convex Repeated Games and Fenchel Duality

We describe and analyze an algorithmic framework for playing convex repeatedgames. In each trial of the repeated game, the first player predicts a vector andthen the second player responds with a loss function over the vector. Based on ageneralization of Fenchel duality, we derive an algorithmic framework for the firstplayer and analyze the player’s regret. We then use our algorithmic framework andits corresponding regret analysis for online learning problems and for boosting.