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

TL;DR

This paper introduces an efficient learning method for extensive-form games that achieves near-logarithmic trigger regret growth, significantly improving convergence rates to equilibrium concepts compared to previous approaches.

Contribution

It presents a novel uncoupled learning dynamic with $O( ext{log } T)$ trigger regret, settling an open problem and enhancing convergence guarantees in extensive-form games.

Findings

Trigger regret grows as $O( ext{log } T)$ for all players.

Guarantees convergence to extensive-form correlated equilibria at rate $rac{ ext{log } T}{T}$.

Introduces a refined regret circuit preserving the RVU property.

Abstract

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.