Simple Uncoupled No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium

• URL: http://arxiv.org/abs/2104.01520v1
• Date: Sun, 4 Apr 2021 02:26:26 GMT
• Title: Simple Uncoupled No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium
• Authors: Gabriele Farina, Andrea Celli, Alberto Marchesi, Nicola Gatti
• Abstract summary: We study the existence of simple, uncoupled no-regret dynamics that converge to correlated equilibria in normal-form games. We introduce a notion of trigger regret in extensive-form games, which extends that of internal regret in normal-form games. We give an efficient no-regret algorithm which guarantees with high probability that trigger regrets grow sublinearly in the number of iterations.
• Score: 65.64512759706271
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The existence of simple, uncoupled no-regret dynamics that converge to correlated equilibria in normal-form games is a celebrated result in the theory of multi-agent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repeated normal-form game, the empirical frequency of play converges to a normal-form correlated equilibrium. Extensive-form (that is, tree-form) games generalize normal-form games by modeling both sequential and simultaneous moves, as well as private information. Because of the sequential nature and presence of partial information in the game, extensive-form correlation possesses significantly different properties than the normal-form counterpart, many of which are still open research directions. Extensive-form correlated equilibrium (EFCE) has been proposed as the natural extensive-form counterpart to normal-form correlated equilibrium, though it was currently unknown whether EFCE emerges as the result of uncoupled agent dynamics. In this article, we give the first uncoupled no-regret dynamics that converge with high probability to the set of EFCEs in n-player general-sum extensive-form games with perfect recall. First, we introduce a notion of trigger regret in extensive-form games, which extends that of internal regret in normal-form games. When each player has low trigger regret, the empirical frequency of play is close to an EFCE. Then, we give an efficient no-regret algorithm which guarantees with high probability that trigger regrets grow sublinearly in the number of iterations.

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