Fast swap regret minimization and applications to approximate correlated equilibria

Abstract

We give a simple and computationally efficient algorithm that, for any constant >0, obtains T-swap regret within only T = polylog(n) rounds; this is an exponential improvement compared to the super-linear number of rounds required by the state-of-the-art algorithm, and resolves the main open problem of [Blum and Mansour 2007]. Our algorithm has an exponential dependence on , but we prove a new, matching lower bound. Our algorithm for swap regret implies faster convergence to -Correlated Equilibrium (-CE) in several regimes: For normal form two-player games with n actions, it implies the first uncoupled dynamics that converges to the set of -CE in polylogarithmic rounds; a polylog(n)-bit communication protocol for -CE in two-player games (resolving an open problem mentioned by [Babichenko-Rubinstein'2017, Goos-Rubinstein'2018, Ganor-CS'2018]); and an O(n)-query algorithm for -CE (resolving an open problem of [Babichenko'2020] and obtaining the first separation between -CE and -Nash equilibrium in the query complexity model). For extensive-form games, our algorithm implies a PTAS for normal form correlated equilibria, a solution concept often conjectured to be computationally intractable (e.g. [Stengel-Forges'08, Fujii'23]).

Tasks

Reproductions