Disturbance Decoupling for Gradient-Based Multi-Agent Learning With Quadratic Costs

Motivated by applications of multi-agent learning in noisy environments, this letter studies the robustness gradient-based dynamics with respect to disturbances. While disturbances injected along a coordinate corresponding any individual player's actions can always affect overall dynamics, subset players be disturbance decoupled-i.e., such players' are completely unaffected disturbance. We provide necessary and sufficient conditions guarantee property for games quadratic cost functions, which encompass one-shot continuous games, finite-horizon linear (LQ) dynamic bilinear games. Specifically, decoupling is characterized both algebraic graph-theoretic on latter obtained constructing game graph based gradients costs. For LQ we show that imposes constraints controllable unobservable subspaces players. two player within action coordinates payoff matrices. Illustrative numerical examples provided.