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

We propose efficient no-regret learning dynamics and ellipsoid-based methods for computing linear correlated equilibriaunicodex2014a relaxation of correlated equilibria and a strengthening of coarse correlated equilibriaunicodex2014in 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.