  Federated learning (FL) is a prospective distributed machine learning
framework that can preserve data privacy. In particular, cross-silo FL can
complete model training by making isolated data islands of different
organizations collaborate with a parameter server (PS) via exchanging model
parameters for multiple communication rounds. In cross-silo FL, an incentive
mechanism is indispensable for motivating data owners to contribute their
models to FL training. However, how to allocate the reward budget among
different rounds is an essential but complicated problem largely overlooked by
existing works. The challenge of this problem lies in the opaque feedback
between reward budget allocation and model utility improvement of FL, making
the optimal reward budget allocation complicated. To address this problem, we
design an online reward budget allocation algorithm using Bayesian optimization
named BARA (\underline{B}udget \underline{A}llocation for \underline{R}everse
\underline{A}uction). Specifically, BARA can model the complicated relationship
between reward budget allocation and final model accuracy in FL based on
historical training records so that the reward budget allocated to each
communication round is dynamically optimized so as to maximize the final model
utility. We further incorporate the BARA algorithm into reverse auction-based
incentive mechanisms to illustrate its effectiveness. Extensive experiments are
conducted on real datasets to demonstrate that BARA significantly outperforms
competitive baselines by improving model utility with the same amount of reward
budget.
