# Weighted Distributed Differential Privacy ERM: Convex and Non-convex

arXiv: https://arxiv.org/abs/1910.10308 · HTML: https://mlsanity.com/paper/1910.10308/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2019.

## Built on by (most cited first, 3 of 3)

- [Private Non-Convex Federated Learning Without a Trusted Server](https://mlsanity.com/paper/2203.06735/) (2022)
- [Differentially Private Non-convex Learning for Multi-layer Neural Networks](https://mlsanity.com/paper/2310.08425/) (2023)
- [How to Make the Gradients Small Privately: Improved Rates for Differentially Private Non-Convex Optimization](https://mlsanity.com/paper/2402.11173/) (2024)

## Abstract (arXiv)

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.