Contextual Games: Multi-Agent Learning with Side Information
This work addresses the problem of multi-agent learning with side information for applications like traffic routing, presenting a novel framework but with incremental algorithmic contributions.
The paper introduces contextual games, a new class of repeated games that incorporate contextual information at each round, and proposes a kernel-based online algorithm to minimize contextual regret, showing empirically in a traffic routing experiment that it improves performance and welfare compared to baselines.
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.