Efficient Learning and Computation of Linear Correlated Equilibrium in General Convex Games

TL;DR

This paper introduces efficient algorithms for computing and learning linear correlated equilibria in general convex games, which include complex scenarios like extensive-form games, advancing the understanding of equilibrium computation.

Contribution

It extends existing frameworks to enable polynomial-time computation and learning of linear correlated equilibria in broad classes of convex games, even with intractable deviation sets.

Findings

Linear correlated equilibria are the tightest polynomial-time computable equilibrium notion.

The proposed algorithms work efficiently even when deviation sets are intractable.

Extensions to existing frameworks enable equilibrium computation without access to separation oracles.

Abstract

We propose efficient no-regret learning dynamics and ellipsoid-based methods for computing linear correlated equilibria$\unicode{x2014}$a relaxation of correlated equilibria and a strengthening of coarse correlated equilibria$\unicode{x2014}$in general convex games. These are games where the number of pure strategies is potentially exponential in the natural representation of the game, such as extensive-form games. Our work identifies linear correlated equilibria as the tightest known notion of equilibrium that is computable in polynomial time and is efficiently learnable for general convex games. Our results are enabled by a generalization of the seminal framework of of Gordon et al. [2008] for $\Phi$-regret minimization, providing extensions to this framework that can be used even when the set of deviations $\Phi$ is intractable to separate/optimize over. Our polynomial-time algorithms are similarly enabled by extending the Ellipsoid-Against-Hope approach of Papadimitriou and Roughgarden [2008] and its generalization to games of non-polynomial type proposed by Farina and Pipis [2024a]. We provide an extension to these approaches when we do not have access to the separation oracles required by these works for the dual player.