Nasser Aldaghri, Hessam Mahdavifar, Ahmad Beirami
Federated learning (FL) takes a first step towards privacy-preserving machine learning by training models while keeping client data local. Models trained using FL may still leak private client information through model updates during training. Differential privacy (DP) may be employed on model updates to provide privacy guarantees within FL, typically at the cost of degraded performance of the final trained model. Both non-private FL and DP-FL can be solved using variants of the federated averaging (FedAvg) algorithm. In this work, we consider a heterogeneous DP setup where clients require varying degrees of privacy guarantees. First, we analyze the optimal solution to the federated linear regression problem with heterogeneous DP in a Bayesian setup. We find that unlike the non-private setup, where the optimal solution for homogeneous data amounts to a single global solution for all clients learned through FedAvg, the optimal solution for each client in this setup would be a personalized one even for homogeneous data. We also analyze the privacy-utility trade-off for this setup, where we characterize the gain obtained from heterogeneous privacy where some clients opt for less strict privacy guarantees. We propose a new algorithm for FL with heterogeneous DP, named FedHDP, which employs personalization and weighted averaging at the server using the privacy choices of clients, to achieve better performance on clients' local models. Through numerical experiments, we show that FedHDP provides up to $9.27\%$ performance gain compared to the baseline DP-FL for the considered datasets where $5\%$ of clients opt out of DP. Additionally, we show a gap in the average performance of local models between non-private and private clients of up to $3.49\%$, empirically illustrating that the baseline DP-FL might incur a large utility cost when not all clients require the stricter privacy guarantees.