Convex Repeated Games and Fenchel Duality
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We describe and analyze an algorithmic framework for playing convex repeated games. In each trial of the repeated game, the first player predicts a vector and then the second player responds with a loss function for the vector. We describe a generalization of Fenchel duality, which is used to derive an algorithmic framework for the first player and analyze the player's regret. We then use our algorithmic framework and its corresponding regret analysis for analyzing online learning and boosting algorithms.
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