Near-Optimal $Φ$-Regret Learning in Extensive-Form Games
This work addresses a fundamental problem in game theory and multi-agent learning by providing near-optimal regret bounds for extensive-form games, which is incremental but significant for the field.
The paper tackles the problem of learning in multiplayer extensive-form games by establishing efficient and uncoupled dynamics that achieve trigger regret of O(log T), improving exponentially over the prior O(T^{1/4}) bound and settling an open question, with immediate consequences for near-optimal convergence to correlated equilibria at a rate of log T/T.
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 $O(T^{1/4})$, 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 $\frac{\log T}{T}$. 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.