  Federated Learning (FL) is a distributed learning framework that can deal
with the distributed issue in machine learning and still guarantee high
learning performance. However, it is impractical that all users will sacrifice
their resources to join the FL algorithm. This motivates us to study the
incentive mechanism design for FL. In this paper, we consider a FL system that
involves one base station (BS) and multiple mobile users. The mobile users use
their own data to train the local machine learning model, and then send the
trained models to the BS, which generates the initial model, collects local
models and constructs the global model. Then, we formulate the incentive
mechanism between the BS and mobile users as an auction game where the BS is an
auctioneer and the mobile users are the sellers. In the proposed game, each
mobile user submits its bids according to the minimal energy cost that the
mobile users experiences in participating in FL. To decide winners in the
auction and maximize social welfare, we propose the primal-dual greedy auction
mechanism. The proposed mechanism can guarantee three economic properties,
namely, truthfulness, individual rationality and efficiency. Finally, numerical
results are shown to demonstrate the performance effectiveness of our proposed
mechanism.
