  Federated learning (FL) serves as a data privacy-preserved machine learning
paradigm, and realizes the collaborative model trained by distributed clients.
To accomplish an FL task, the task publisher needs to pay financial incentives
to the FL server and FL server offloads the task to the contributing FL
clients. It is challenging to design proper incentives for the FL clients due
to the fact that the task is privately trained by the clients. This paper aims
to propose a contract theory based FL task training model towards minimizing
incentive budget subject to clients being individually rational (IR) and
incentive compatible (IC) in each FL training round. We design a
two-dimensional contract model by formally defining two private types of
clients, namely data quality and computation effort. To effectively aggregate
the trained models, a contract-based aggregator is proposed. We analyze the
feasible and optimal contract solutions to the proposed contract model.
%Experimental results demonstrate that the proposed framework and contract
model can effective improve the generation accuracy of FL tasks. Experimental
results show that the generalization accuracy of the FL tasks can be improved
by the proposed incentive mechanism where contract-based aggregation is
applied.
