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

From Poincar\'e Recurrence to Convergence in Imperfect Information Games: Finding Equilibrium via Regularization