Weighted Distributed Differential Privacy ERM: Convex and Non-convex

TL;DR

This paper introduces a weighted distributed differential privacy ERM method that improves privacy guarantees and model performance in distributed machine learning, especially with uneven client data scales, and extends to non-convex loss functions.

Contribution

It proposes a novel weighted gradient perturbation approach for differential privacy in distributed ERM, applicable to convex and non-convex loss functions, with theoretical and empirical validation.

Findings

Improved noise and excess risk bounds with weighted clients.

Enhanced model performance on real datasets with uneven data distribution.

State-of-the-art gradient perturbation in distributed differential privacy.

Abstract

Distributed machine learning is an approach allowing different parties to learn a model over all data sets without disclosing their own data. In this paper, we propose a weighted distributed differential privacy (WD-DP) empirical risk minimization (ERM) method to train a model in distributed setting, considering different weights of different clients. We guarantee differential privacy by gradient perturbation, adding Gaussian noise, and advance the state-of-the-art on gradient perturbation method in distributed setting. By detailed theoretical analysis, we show that in distributed setting, the noise bound and the excess empirical risk bound can be improved by considering different weights held by multiple parties. Moreover, considering that the constraint of convex loss function in ERM is not easy to achieve in some situations, we generalize our method to non-convex loss functions which satisfy Polyak-Lojasiewicz condition. Experiments on real data sets show that our method is more reliable and we improve the performance of distributed differential privacy ERM, especially in the case that data scale on different clients is uneven.