Communication-Efficient Distributed Learning for Nash Equilibrium of Aggregative Games Over Time-Varying Digraphs

Communication efficiency is a major challenge in learning the Nash equilibrium (NE) of aggregative games in a distributed manner. To address this problem, this article focuses on designing a communication-efficient algorithm under unbalanced digraphs, where the cost function of each player is affected by its own actions and the average aggregation function. In particular, the considered games have no central node, and no player has direct access to the aggregation function. To estimate the aggregation function, an auxiliary variable is employed to estimate the right Perron eigenvector of the column-stochastic weight matrix, which extends the dynamic average consensus protocol to time-varying digraphs. Additionally, players exchange information periodically and perform multistep local updates with local information between two consecutive communications. By combining the above two strategies with the gradient descent method, a communication-efficient algorithm is proposed and achieves a linear convergence rate. Then, the communication period selection method is provided to determine the best tradeoff between local updates and information exchange under limited resources. Finally, numerical results demonstrate the effectiveness of the proposed algorithm.