# Mediator Interpretation and Faster Learning Algorithms for Linear Correlated Equilibria in General Extensive-Form Games

arXiv: https://arxiv.org/abs/2310.15935 · HTML: https://mlsanity.com/paper/2310.15935/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2023.

## Built on by (most cited first, 3 of 3)

- [Swap Regret and Correlated Equilibria Beyond Normal-Form Games](https://mlsanity.com/paper/2502.20229/) (2025)
- [Expected Variational Inequalities](https://mlsanity.com/paper/2502.18605/) (2025)
- [Swap Regret Minimization Through Response-Based Approachability](https://mlsanity.com/paper/2602.06264/) (2026)

## Abstract (arXiv)

A recent paper by Farina & Pipis (2023) established the existence of uncoupled no-linear-swap regret dynamics with polynomial-time iterations in extensive-form games. The equilibrium points reached by these dynamics, known as linear correlated equilibria, are currently the tightest known relaxation of correlated equilibrium that can be learned in polynomial time in any finite extensive-form game. However, their properties remain vastly unexplored, and their computation is onerous. In this paper, we provide several contributions shedding light on the fundamental nature of linear-swap regret. First, we show a connection between linear deviations and a generalization of communication deviations in which the player can make queries to a "mediator" who replies with action recommendations, and, critically, the player is not constrained to match the timing of the game as would be the case for communication deviations. We coin this latter set the untimed communication (UTC) deviations. We show that the UTC deviations coincide precisely with the linear deviations, and therefore that any player minimizing UTC regret also minimizes linear-swap regret. We then leverage this connection to develop state-of-the-art no-regret algorithms for computing linear correlated equilibria, both in theory and in practice. In theory, our algorithms achieve polynomially better per-iteration runtimes; in practice, our algorithms represent the state of the art by several orders of magnitude.