# Differentially Private Distributed Convex Optimization

arXiv: https://arxiv.org/abs/2302.14514 · HTML: https://mlsanity.com/paper/2302.14514/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 55 references that are in the map.
- First posted on arXiv 28 Feb 2023.

## Builds on (most cited first, 27 of 27)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [iDLG: Improved Deep Leakage from Gradients](https://mlsanity.com/paper/2001.02610/) (2020)
- [A Survey on Federated Learning Systems: Vision, Hype and Reality for Data Privacy and Protection](https://mlsanity.com/paper/1907.09693/) (2019)
- [FedML: A Research Library and Benchmark for Federated Machine Learning](https://mlsanity.com/paper/2007.13518/) (2020)
- [cpSGD: Communication-efficient and differentially-private distributed SGD](https://mlsanity.com/paper/1805.10559/) (2018)
- [Gradient Inversion with Generative Image Prior](https://mlsanity.com/paper/2110.14962/) (2021)
- [Fairness-aware Agnostic Federated Learning](https://mlsanity.com/paper/2010.05057/) (2020)
- [Local and Central Differential Privacy for Robustness and Privacy in Federated Learning](https://mlsanity.com/paper/2009.03561/) (2020)
- [Satisfying Real-world Goals with Dataset Constraints](https://mlsanity.com/paper/1606.07558/) (2016)
- [On the Linear Convergence of the ADMM in Decentralized Consensus Optimization](https://mlsanity.com/paper/1307.5561/) (2013)
- [Imposing Hard Constraints on Deep Networks: Promises and Limitations](https://mlsanity.com/paper/1706.02025/) (2017)
- [DP-ADMM: ADMM-based Distributed Learning with Differential Privacy](https://mlsanity.com/paper/1808.10101/) (2018)
- [Controlled Sparsity via Constrained Optimization or: How I Learned to Stop Tuning Penalties and Love Constraints](https://mlsanity.com/paper/2208.04425/) (2022)
- [Hybrid Differentially Private Federated Learning on Vertically Partitioned Data](https://mlsanity.com/paper/2009.02763/) (2020)
- [APPFL: Open-Source Software Framework for Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2202.03672/) (2022)
- [Communication-Efficient ADMM-based Federated Learning](https://mlsanity.com/paper/2110.15318/) (2021)
- [Differentially Private ADMM for Convex Distributed Learning: Improved Accuracy via Multi-Step Approximation](https://mlsanity.com/paper/2005.07890/) (2020)
- [A Privacy-Preserving Distributed Control of Optimal Power Flow](https://mlsanity.com/paper/2102.02276/) (2021)
- [Differentially Private Distributed Optimal Power Flow](https://mlsanity.com/paper/1910.10136/) (2019)
- [An Extragradient-Based Alternating Direction Method for Convex Minimization](https://mlsanity.com/paper/1301.6308/) (2013)
- [Data Centers as Dispatchable Loads to Harness Stranded Power](https://mlsanity.com/paper/1606.00350/) (2016)

## Abstract (arXiv)

This paper considers distributed optimization (DO) where multiple agents cooperate to minimize a global objective function, expressed as a sum of local objectives, subject to some constraints. In DO, each agent iteratively solves a local optimization model constructed by its own data and communicates some information (e.g., a local solution) with its neighbors until a global solution is obtained. Even though locally stored data are not shared with other agents, it is still possible to reconstruct the data from the information communicated among agents, which could limit the practical usage of DO in applications with sensitive data. To address this issue, we propose a privacy-preserving DO algorithm for constrained convex optimization models, which provides a statistical guarantee of data privacy, known as differential privacy, and a sequence of iterates that converges to an optimal solution in expectation. The proposed algorithm generalizes a linearized alternating direction method of multipliers by introducing a multiple local updates technique to reduce communication costs and incorporating an objective perturbation method in the local optimization models to compute and communicate randomized feasible local solutions that cannot be utilized to reconstruct the local data, thus preserving data privacy. Under the existence of convex constraints, we show that, while both algorithms provide the same level of data privacy, the objective perturbation used in the proposed algorithm can provide better solutions than does the widely adopted output perturbation method that randomizes the local solutions by adding some noise. We present the details of privacy and convergence analyses and numerically demonstrate the effectiveness of the proposed algorithm by applying it in two different applications, namely, distributed control of power flow and federated learning, where data privacy is of concern.