Near-Optimal Phi-Regret Learning in Extensive-Form Games

In this paper, we establish efficient and uncoupled learning dynamics so that, when employed by all players in multiplayer perfect-recall imperfect-information extensive-form games, the trigger regret of each player grows as O(log T) after T repetitions of play. This improves exponentially over the prior best known trigger-regret bound of O(T1/4), and settles a recent open question by Bai et al. (2022). As an immediate consequence, we guarantee convergence to the set of extensive-form correlated equilibria and coarse correlated equilibria at a near-optimal rate of fraclog TT. Building on prior work, at the heart of our construction lies a more general result regarding fixed points deriving from rational functions with polynomial degree, a property that we establish for the fixed points of (coarse) trigger deviation functions. Moreover, our construction leverages a refined regret circuit for the convex hull, which -- unlike prior guarantees -- preserves the RVU property introduced by Syrgkanis et al. (NIPS, 2015); this observation has an independent interest in establishing near-optimal regret under learning dynamics based on a CFR-type decomposition of the regret.