FedLAP-DP: Federated Learning by Sharing Differentially Private Loss Approximations

This work proposes FedLAP-DP, a novel privacy-preserving approach for federated learning. Unlike previous linear point-wise gradient-sharing schemes, such as FedAvg, our formulation enables a type of global optimization by leveraging synthetic samples received from clients. We additionally introduce an approach to measure effective approximation regions reflecting the quality of the approximation. Therefore, the server can recover an approximation of the global loss landscape and optimize the model globally. Moreover, motivated by the emerging privacy concerns, we demonstrate that our approach seamlessly works with record-level differential privacy (DP), granting theoretical privacy guarantees for every data record on the clients. Extensive results validate the efficacy of our formulation on various datasets with highly skewed distributions. Our method consistently improves over the baselines, especially considering highly skewed distributions and noisy gradients due to DP. The source code and setup will be released upon publication. Federated Learning (FL) (McMahan et al., 2017) is a distributed learning framework that allows participants to train a model collaboratively without sharing their data. Predominantly, existing works (McMahan et al., 2017; Karimireddy et al., 2020; Li et al., 2020) achieve this by training local models on clients' private datasets and sharing only the gradients with the central server. Despite extensive research over the past few years, these prevalent gradient-based methods still suffer from several challenges (Kairouz et al., 2021), such as data heterogeneity, potential risks of privacy breaches, and high communication costs.