A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Games

Samuel Sokota, Ryan D'Orazio, J Zico Kolter, Nicolas Loizou, Marc Lanctot, Ioannis Mitliagkas, Noam Brown, Christian Kroer

Keywords: reinforcement learning, quantal response equilibria, two-player zero-sum games, mirror descent, variational inequalities, Nash equilibria, algorithmic game theory, proximal gradient

TL;DR: A single algorithm for both single-agent reinforcement learning and approximating quantal response and Nash equilibria in two-player zero-sum games.

Abstract: This work studies an algorithm, which we call magnetic mirror descent, that is inspired by mirror descent and the non-Euclidean proximal gradient algorithm. Our contribution is demonstrating the virtues of magnetic mirror descent as both an equilibrium solver and as an approach to reinforcement learning in two-player zero-sum games. These virtues include: 1) Being the first quantal response equilibria solver to achieve linear convergence for extensive-form games with first order feedback; 2) Being the first standard reinforcement learning algorithm to achieve empirically competitive results with CFR in tabular settings; 3) Achieving favorable performance in 3x3 Dark Hex and Phantom Tic-Tac-Toe as a self-play deep reinforcement learning algorithm.

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