Regret-minimizing algorithms are an important class of machine learning
algorithms that are closely related to game theoretic equilibria (e.g., Nash
equilibria, correlated equilibria).  In this work we present a general
framework in which we derive a class of ``no-regret'' learning algorithms that
converge to a corresponding set of equilibria.  We show how to extend these
algorithms to the more difficult naive setting.  We also extend our framework
to the case of convex games, providing the basis for a class of algorithms
which can be exponentially faster than previously known convex algorithms.
Finally, we apply our framework to the class of extensive-form games to derive
the first class of algorithms that learn the set of extensive-form correlated
equilibria.