Distributed Online Learning Algorithm for Noncooperative Games Over Unbalanced Digraphs

This article investigates constrained online noncooperative games (NGs) of multiagent systems over unbalanced digraphs, where the cost functions of players are time-varying and are gradually revealed to corresponding players only after decisions are made. Moreover, in the problem, the players are subject to local convex set constraints and time-varying coupling nonlinear inequality constraints. To the best of our knowledge, no result about online games with unbalanced digraphs has been reported, let alone constrained online games. To seek the variational generalized Nash equilibrium (GNE) of the game online, a distributed learning algorithm is proposed based on gradient descent, projection, and primal-dual methods. Under the algorithm, sublinear dynamic regrets and constraint violations are established. Finally, online electricity market games illustrate the algorithm.