# Differentially Private Distributed Optimization

arXiv: https://arxiv.org/abs/1401.2596 · HTML: https://mlsanity.com/paper/1401.2596/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2014.

## Built on by (most cited first, 24 of 24)

- [Muffliato: Peer-to-Peer Privacy Amplification for Decentralized Optimization and Averaging](https://mlsanity.com/paper/2206.05091/) (2022)
- [Decentralized Stochastic Optimization with Inherent Privacy Protection](https://mlsanity.com/paper/2205.03884/) (2022)
- [Decentralized Nonconvex Optimization with Guaranteed Privacy and Accuracy](https://mlsanity.com/paper/2212.07534/) (2022)
- [Differentially Private Decentralized Learning with Random Walks](https://mlsanity.com/paper/2402.07471/) (2024)
- [Privacy Attacks in Decentralized Learning](https://mlsanity.com/paper/2402.10001/) (2024)
- [Quantization enabled Privacy Protection in Decentralized Stochastic Optimization](https://mlsanity.com/paper/2208.04845/) (2022)
- [Communication efficient privacy-preserving distributed optimization using adaptive differential quantization](https://mlsanity.com/paper/2105.14416/) (2021)
- [Distributed Sketching for Randomized Optimization: Exact Characterization, Concentration and Lower Bounds](https://mlsanity.com/paper/2203.09755/) (2022)
- [PersA-FL: Personalized Asynchronous Federated Learning](https://mlsanity.com/paper/2210.01176/) (2022)
- [Distributed Online Private Learning of Convex Nondecomposable Objectives](https://mlsanity.com/paper/2206.07944/) (2022)
- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [From Centralized to Decentralized Federated Learning: Theoretical Insights, Privacy Preservation, and Robustness Challenges](https://mlsanity.com/paper/2503.07505/) (2025)
- [Locally Differentially Private Gradient Tracking for Distributed Online Learning over Directed Graphs](https://mlsanity.com/paper/2310.16105/) (2023)
- [Privacy-Preserving Distributed Optimization and Learning](https://mlsanity.com/paper/2403.00157/) (2024)
- [Differential Privacy Analysis of Decentralized Gossip Averaging under Varying Threat Models](https://mlsanity.com/paper/2505.19969/) (2025)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [Unified Privacy Guarantees for Decentralized Learning via Matrix Factorization](https://mlsanity.com/paper/2510.17480/) (2025)
- [Locally Differentially Private Distributed Online Learning with Guaranteed Optimality](https://mlsanity.com/paper/2306.14094/) (2023)
- [Characterizing the Accuracy-Communication-Privacy Trade-off in Distributed Stochastic Convex Optimization](https://mlsanity.com/paper/2501.03222/) (2025)
- [Private Networked Federated Learning for Nonsmooth Objectives](https://mlsanity.com/paper/2306.14012/) (2023)
- [Near-optimal Differentially Private Client Selection in Federated Settings](https://mlsanity.com/paper/2310.09370/) (2023)
- [Differentially Private Equilibrium Finding in Polymatrix Games](https://mlsanity.com/paper/2503.09538/) (2025)
- [Event-Driven Online Vertical Federated Learning](https://mlsanity.com/paper/2506.14911/) (2025)
- [A Weighted Gradient Tracking Privacy-Preserving Method for Distributed Optimization](https://mlsanity.com/paper/2509.18134/) (2025)

## Abstract (arXiv)

In distributed optimization and iterative consensus literature, a standard problem is for N agents to minimize a function f over a subset of Euclidean space, where the cost function is expressed as a sum sum fi. In this paper, we study the private distributed optimization (PDOP) problem with the additional requirement that the cost function of the individual agents should remain differentially private. The adversary attempts to infer information about the private cost functions from the messages that the agents exchange. Achieving differential privacy requires that any change of an individual's cost function only results in unsubstantial changes in the statistics of the messages. We propose a class of iterative algorithms for solving PDOP, which achieves differential privacy and convergence to the optimal value. Our analysis reveals the dependence of the achieved accuracy and the privacy levels on the the parameters of the algorithm. We observe that to achieve ε-differential privacy the accuracy of the algorithm has the order of O(frac1ε2).