Convex Repeated Games and Fenchel Duality
Shai Shalev-Shwartz and Yoram Singer
In: NIPS 2006, 4-10 Dec 2006, Vancouver, CA.
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 over the vector. Based on a generalization of Fenchel duality,
we 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 online
learning problems and for boosting.