Distributed Online Learning Algorithms for Aggregative Games Over Time-Varying Unbalanced Digraphs

In this paper, online aggregative games over time-varying unbalanced digraphs are studied, where the cost functions of players are time-varying and are gradually revealed to corresponding players only after decisions are made. Moreover, in the problems, players are subject to local convex set constraints and time-varying coupled 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 solve the problem, a distributed online algorithm based on primal-dual, mirror descents and push-sum methods is developed. With the algorithm, sublinear dynamic regrets and constraint violations are established. Finally, online electricity market games illustrate the algorithm.