Abstract

A general class of no-regret learning algorithms, called - no-regret learning algorithms is defined, which spans the spectrum from no-internal-regret learning to no-external-regret learning, and beyond. describes the set of strategies to which the play of a learning algorithm is compared: a learning algorithm satisfies -no-regret iff no regret is experienced for playing as the algorithm prescribes, rather than playing according to any of the transformations of the algorithm's play prescribed by elements of . Analogously, a class of game-theoretic equilibria, called -equilibria, is defined, and it is shown that the empirical distribution of play of -no-regret algorithms converges to the set of -equilibria.

Citations