We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to 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 $O(T^{-1/2})$ 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.

通过采用具有一种新颖形式的经验回忆的正则化学习算法，我们表明，在多人博弈的普通形式中，该类自适应算法能够实现更快的收敛速率，并实现对近似效率和粗略相关均衡的收敛，并且，对这种类型算法应用的每个玩家，他们的个体后悔降至$O(T^{-3/4})$，而其效用之和则以$O(T^{-1})$的速度趋于近似最优，在与该类算法相对应的算法维持更快的速率的同时，我们还表明了该类中的任何算法均可通过黑匣子降至$	ilde {O}(T^{-1/2})$的速率来抵抗对手。

正则化学习在博弈中的快速收敛