A Two-Stage Incentive Mechanism Design for Quality Optimization of Hierarchical Federated Learning

In this paper, we investigate the aggregated model quality maximization problem in hierarchical federated learning, the decision problem of which is proved NP-complete. We develop the mechanism MaxQ to maximize the sum of local model quality, which consists of two stages. In the first stage, an algorithm based on matching game theory is proposed to associate mobile devices with edge servers, which is proved able to achieve the stability and
$\frac {1}{2}$
-approximation ratio. In the second stage, we design an incentive mechanism based on contract theory to maximize the quality of models submitted by mobile devices to edge servers. Through thorough experiments, we analyse the performance of MaxQ and compare it with the existing mechanisms FAIR and EHFL, under different deep learning models ResNet18, ResNet50 and AlexNet, individually. It is found that the model quality can be improved by 8.20% and 7.81%, 10.47% and 11.87%, 10.98% and 11.97% under different models, respectively.