Online Learning in Periodic Zero-Sum Games
Tanner Fiez, Ryann Sim, Stratis Skoulakis, Georgios Piliouras, Lillian, Ratliff

TL;DR
This paper investigates the behavior of online learning algorithms in periodic zero-sum games, revealing that while time-average convergence can fail, Poincaré recurrence persists despite environmental variations.
Contribution
It introduces a novel analysis demonstrating the robustness of Poincaré recurrence in periodic zero-sum games with fixed equilibria, extending understanding of dynamic behaviors.
Findings
Time-average convergence may fail in periodic zero-sum games.
Poincaré recurrence remains robust despite environmental variations.
Analysis methods generalize to non-autonomous dynamical systems.
Abstract
A seminal result in game theory is von Neumann's minmax theorem, which states that zero-sum games admit an essentially unique equilibrium solution. Classical learning results build on this theorem to show that online no-regret dynamics converge to an equilibrium in a time-average sense in zero-sum games. In the past several years, a key research direction has focused on characterizing the day-to-day behavior of such dynamics. General results in this direction show that broad classes of online learning dynamics are cyclic, and formally Poincar\'{e} recurrent, in zero-sum games. We analyze the robustness of these online learning behaviors in the case of periodic zero-sum games with a time-invariant equilibrium. This model generalizes the usual repeated game formulation while also being a realistic and natural model of a repeated competition between players that depends on exogenous…
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Taxonomy
TopicsGame Theory and Applications · Opinion Dynamics and Social Influence · Advanced Bandit Algorithms Research
