Data pricing for vertical federated learning: an approach based on data contribution

Federated Learning (FedL) emerged as a privacy-aware alternative, creating an effective means for multiple data providers to enable collaboration on training models without accessing the original data. Vertical federated learning (VFedL), as a crucial classification within FedL, has always been primarily utilized to train a machine learning model with non-uniform data from different providers. Despite the VFedL's benefits in facilitating collaborative training models while safeguarding data privacy, it remains a daunting challenge to incentivize more valuable data providers to participate in the VFedL due to the absence of scientific data pricing and precise measurement of data contributions from participants in practical operations. In this paper, we construct a scientific data pricing method based on the participants' data contribution score to federated models, so that all data providers can be compensated fairly. Firstly, an accurate measurement method of the data contribution score of each federated participant to the global model is constructed based on shapely values for Monte Carlo optimization. Then, taking the data contribution score as the input variable, we formulate a data pricing game model based on Stackelberg with the hosts as the leader and the guest as the follower in VFedL. We further solve our model and analyze the guest's optimal data usage strategy based on data contribution score and the hosts' optimal data pricing strategy. Our method has been proven through numerical experiments to precisely assess the data contribution score of participants with the Federated Logistic Regression model. These study findings can also offer management direction for the FedL service providers.