Sublinear Dynamic Regrets for Aggregative Games With Feedback Delays and Communication Delays

In this article, we investigate aggregative game problems in dynamic environments, where the cost functions of players change over time and are revealed gradually after players select their strategies in given strategy sets. Specifically, after selecting strategies, players observe the corresponding cost functions with feedback delays. Moreover, players receive the information of their neighbors with communication delays in weight-unbalanced digraphs. To handle such aggregative game problems, a robust learning algorithm is proposed to track time-varying Nash equilibria. The upper bounds of dynamic regrets are given to illustrate the performance of the proposed algorithm. We quantify the impact of both feedback delays and communication delays on dynamic regrets and give the framework to analyze the convergence of strategies in the case of delays. The proposed algorithm achieves the sublinearity of dynamic regrets in the absence of delays. A numerical example is given to illustrate the efficiency of the proposed learning algorithm.