# Differentially Private Consensus-Based Distributed Optimization

arXiv: https://arxiv.org/abs/1903.07792 · HTML: https://mlsanity.com/paper/1903.07792/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2019.

## Built on by (most cited first, 1 of 1)

- [Straggler-Resilient Differentially-Private Decentralized Learning](https://mlsanity.com/paper/2212.03080/) (2022)

## Abstract (arXiv)

Data privacy is an important concern in learning, when datasets contain sensitive information about individuals. This paper considers consensus-based distributed optimization under data privacy constraints. Consensus-based optimization consists of a set of computational nodes arranged in a graph, each having a local objective that depends on their local data, where in every step nodes take a linear combination of their neighbors' messages, as well as taking a new gradient step. Since the algorithm requires exchanging messages that depend on local data, private information gets leaked at every step. Taking (ε, δ)-differential privacy (DP) as our criterion, we consider the strategy where the nodes add random noise to their messages before broadcasting it, and show that the method achieves convergence with a bounded mean-squared error, while satisfying (ε, δ)-DP. By relaxing the more stringent ε-DP requirement in previous work, we strengthen a known convergence result in the literature. We conclude the paper with numerical results demonstrating the effectiveness of our methods for mean estimation.