A Reward Response Game in the Federated Learning System
Suhan Jiang, Jie Wu · 2021
The emergence of federated learning and the increasingly powerful mobile devices lead to a mobile-crowd machine learning paradigm. In this paper, we consider a mobile-crowd federated learning system that includes a central server and a set of mobile devices. As the model requester, the server motivates all devices to train an accurate model by paying them based on their individual contributions. Each participating device needs to balance between the training rewards and costs for profit maximization. A Stackelberg game is proposed to model interactions between the server and devices. To match with reality, our model takes the training deadline and the device-side upload time into consideration. Based on different definitions of individual contribution, two reward policies, i.e., the size-based policy and accuracy-based policy, are compared. The existence and uniqueness of Stackelberg equilibrium (SE) under both definitions are analyzed, according to which algorithms are proposed to achieve the corresponding SE(s). We show that there is a lower bound of 0.5 on the price of anarchy in the proposed game. We extend our model by considering the uncertainty in the upload time, where each device’s upload time is subject to a normal distribution due to its unstable channel. Numerical evaluations are presented to verify the proposed models.