Fast Convergence of Regularized Learning in Games
(1507.00407)Abstract
We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in a game uses an algorithm from our class, their individual regret decays at $O(T{-3/4})$, while the sum of utilities converges to an approximate optimum at $O(T{-1})$--an improvement upon the worst case $O(T{-1/2})$ rates. We show a black-box reduction for any algorithm in the class to achieve $\tilde{O}(T{-1/2})$ rates against an adversary, while maintaining the faster rates against algorithms in the class. Our results extend those of [Rakhlin and Shridharan 2013] and [Daskalakis et al. 2014], who only analyzed two-player zero-sum games for specific algorithms.
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