In this paper we investigate the Follow the Regularized Leader dynamics in sequential imperfect information games (IIG). We generalize existing results of Poincar\'e recurrence from normal-form games to zero-sum two-player imperfect information games and other sequential game settings. We then investigate how adapting the reward (by adding a regularization term) of the game can give strong convergence guarantees in monotone games. We continue by showing how this reward adaptation technique can be leveraged to build algorithms that converge exactly to the Nash equilibrium. Finally, we show how these insights can be directly used to build state-of-the-art model-free algorithms for zero-sum two-player Imperfect Information Games (IIG).

研究了在顺序不完美信息游戏中遵循规则的领导者动态，推广了 Poincaré 循环结果，并探讨了通过调整奖励来建立收敛保证的技术，进而构建了精确收敛到 Nash 平衡的算法，为零和二人不完美信息游戏的无模型算法提供了新思路。

从庞加莱回归到不完全信息博弈的收敛：通过正则化寻找均衡