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.

翻译：联邦学习（FL）是一种有前景的分布式机器学习框架，能够保护数据隐私。特别是，跨孤岛FL通过让不同组织的孤立数据岛与参数服务器（PS）协作，在多个通信轮次中交换模型参数，从而完成模型训练。在跨孤岛FL中，激励机制对于激励数据所有者将其模型贡献给FL训练不可或缺。然而，如何在不同的轮次之间分配奖励预算是一个重要但复杂的问题，现有研究很大程度上忽视了这一点。该问题的挑战在于奖励预算分配与FL模型效用提升之间的反馈不透明，使得最优奖励预算分配变得复杂。为解决这一问题，我们设计了一种基于贝叶斯优化的在线奖励预算分配算法，命名为BARA（\underline{B}udget \underline{A}llocation for \underline{R}everse \underline{A}uction）。具体而言，BARA能够基于历史训练记录建模FL中奖励预算分配与最终模型精度之间的复杂关系，从而动态优化分配给每个通信轮次的奖励预算，以最大化最终模型效用。我们进一步将BARA算法融入基于反向拍卖的激励机制中，以展示其有效性。在真实数据集上进行了大量实验，结果表明，BARA在相同奖励预算下通过提升模型效用显著优于多个竞争基线。