Incentive Mechanism Design for Federated Learning with Multi-Dimensional Private Information

As an emerging machine learning technique, federated learning has received significant attention recently due to its promising performance in mitigating privacy risks and costs. In federated learning, the model training is distributed over users and coordinated by a central server. Users only need to send the most updated learning model parameters to the server without revealing their private data. While most of the existing work of federated learning focused on designing the learning algorithm to improve the training performance, the incentive issue for encouraging users' participation is still under-explored. Such a fundamental issue can significantly affect the training efficiency, effectiveness, and even the practical operability of federated learning. This paper presents an analytical study on the server's optimal incentive mechanism design, in the presence of users' multi-dimensional private information including training cost and communication delay. Specifically, we consider a multi-dimensional contract-theoretic approach, with a key contribution of summarizing users' multi-dimensional private information into a one-dimensional criterion that allows a complete order of users. We further perform the analysis in three different information scenarios to reveal the impact of the level of information asymmetry on server's optimal strategy and minimum cost. We show that weakly incomplete information does not increase the server's cost. However, the optimal mechanism design under strongly incomplete information is much more challenging, and it is not always optimal for the server to incentivize the group of users with the lowest training cost and delay to participate.