Provable Computational and Statistical Guarantees for Efficient Learning of Continuous-Action Graphical Games

TL;DR

This paper introduces a regularized method for efficiently learning the structure and equilibria of continuous-action graphical games with quadratic payoffs from limited data, with guarantees on accuracy and complexity.

Contribution

It proposes a novel $\,\ell_{12}$-block regularized approach that recovers the true game structure and equilibria with logarithmic sample complexity and polynomial runtime.

Findings

Recovers the true game structure under certain conditions.

Achieves logarithmic sample complexity relative to the number of players.

Runs in polynomial time, making it computationally feasible.

Abstract

In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A continuous-action graphical game can possibly have an uncountable set of Nash euqilibria. We propose a $\ell_{12}-$ block regularized method which recovers a graphical game, whose Nash equilibria are the $\epsilon$-Nash equilibria of the game from which the data was generated (true game). Under a slightly stringent condition on the parameters of the true game, our method recovers the exact structure of the graphical game. Our method has a logarithmic sample complexity with respect to the number of players. It also runs in polynomial time.