Convergence to Nash equilibrium in continuous games with noisy first-order feedback

International audienceThis paper examines the convergence of a broad classof distributed learning dynamics for games with continuous actionsets. The dynamics under study comprise a multi-agent generalization of Nesterov’s dual averaging (DA) method, a primal-dualmirror descent method that has recently seen a major resurgencein the field of large-scale optimization and machine learning. Toaccount for settings with high temporal variability and uncertainty, we adopt a continuous-time formulation of dual averagingand we investigate the dynamics’ long-run behavior when playershave either noiseless or noisy information on their payoffgradients. In both the deterministic and stochastic regimes, we establishsublinear rates of convergence of actual and averaged trajectoriesto Nash equilibrium under a variational stability condition