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

• URL: http://arxiv.org/abs/2002.08456v1
• Date: Wed, 19 Feb 2020 21:36:58 GMT
• Title: From Poincar\'e Recurrence to Convergence in Imperfect Information Games: Finding Equilibrium via Regularization
• Authors: Julien Perolat, Remi Munos, Jean-Baptiste Lespiau, Shayegan Omidshafiei, Mark Rowland, Pedro Ortega, Neil Burch, Thomas Anthony, David Balduzzi, Bart De Vylder, Georgios Piliouras, Marc Lanctot, Karl Tuyls
• Abstract summary: We show how adapting the reward can give strong convergence guarantees in monotone games. We also show how this reward adaptation technique can be leveraged to build algorithms that converge exactly to the Nash equilibrium.
• Score: 49.368421783733815
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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).

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