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 equilibria—a relaxation of correlated equilibria and a strengthening of coarse correlated equilibria—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 Gordon et al. [2008] for Φ-regret minimization, providing extensions to this framework that can be used even when the set of deviations Φ 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. This work will appear in STOC 2025, [Daskalakis et al., 2025].

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2025

Author dc:creator

• Pipis, Charilaos

Advisors dc:contributor.advisor

• Daskalakis, Constantinos
• Farina, Gabriele

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/163683

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/163683