  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.
