Contextual Games: Multi-Agent Learning with Side Information

TL;DR

This paper introduces a new class of repeated games called contextual games, leveraging side information and kernel-based methods to improve multi-agent learning, with theoretical guarantees and empirical validation in traffic routing.

Contribution

It formulates the concept of contextual games, proposes an online algorithm exploiting context correlations, and defines new equilibrium notions with convergence guarantees.

Findings

The proposed algorithm achieves lower regret in experiments.

Exploiting contextual information improves overall welfare.

Empirical results show better performance than baselines.

Abstract

We formulate the novel class of contextual games, a type of repeated games driven by contextual information at each round. By means of kernel-based regularity assumptions, we model the correlation between different contexts and game outcomes and propose a novel online (meta) algorithm that exploits such correlations to minimize the contextual regret of individual players. We define game-theoretic notions of contextual Coarse Correlated Equilibria (c-CCE) and optimal contextual welfare for this new class of games and show that c-CCEs and optimal welfare can be approached whenever players' contextual regrets vanish. Finally, we empirically validate our results in a traffic routing experiment, where our algorithm leads to better performance and higher welfare compared to baselines that do not exploit the available contextual information or the correlations present in the game.