Bandwidth Allocation for Low-Latency Wireless Federated Learning: An Evolutionary Game Approach

As a new distributed data training framework, federated learning (FL) has attracted increasing attention owing to its advantages of preserving data privacy and low communication cost. However, in a wireless FL network, due to the limited bandwidth resources, when a large number of clients participate in FL, the communication burden is too heavy. Therefore, efficient bandwidth allocation is critical to facilitate the application of wireless FL. In this paper, we investigate bandwidth allocation in wireless FL networks with the objective of minimizing the latency of FL services. We first analyze and formulate the latency minimization problem. Then, considering that the computing and transmitting capabilities of each client cannot be completely and truly acquired, we develop an evolutionary game (EG) framework to model the dynamic process of bandwidth allocation in wireless FL. We further show the optimal bandwidth allocation solution is equivalent to the evolutionary equilibrium (EE) obtained by the replicator dynamics in the EG model, and prove the EE is asymptotically stable. With the help of these results, we propose the EG-based bandwidth allocation algorithm, which enables the latency of FL services to be reduced by performing the replicator dynamics iteratively. Numerical simulations are provided to demonstrate the evolutionary behaviors in the EG-based bandwidth allocation Algorithm.