A General Class of No-Regret Learning Algorithms and Game-Theoretic Equilibria

A general class of no-regret learning algorithms, called no-Φ-regret learning algorithms, is defined which spans the spectrum from no-external-regret learning to no-internal-regret learning and beyond. The set Φ describes the set of strategies to which the play of a given learning algorithm is compared. A learning algorithm satisfies no-Φ-regret if no regret is experienced for playing as the algorithm prescribes, rather than playing according to any of the strategies that arise by transforming the algorithm’s play via the elements of Φ. We establish the existence of no-Φ-regret algorithms for the class of linear transformations. Analogously, a class of game-theoretic equilibria, called Φ-equilibria, is defined, and it is shown that the empirical distribution of play of no-Φ-regret algorithms converges to the set of Φ-equilibria. A necessary condition for convergence to this set is also derived. Perhaps surprisingly, for the class of linear transformations, the strongest f...

• Type: Conference
• Year: 2003
• Where: COLT
• Authors: Amy R. Greenwald, Amir Jafari
• Keywords: Algorithms, COLT 2003, Learning Algorithm, No-Φ-regret Algorithms