# Differentially Private Distributed Convex Optimization via Functional Perturbation

arXiv: https://arxiv.org/abs/1512.00369 · HTML: https://mlsanity.com/paper/1512.00369/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2015.

## Built on by (most cited first, 11 of 11)

- [Communication efficient privacy-preserving distributed optimization using adaptive differential quantization](https://mlsanity.com/paper/2105.14416/) (2021)
- [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)
- [Privacy-preserving Non-negative Matrix Factorization with Outliers](https://mlsanity.com/paper/2211.01451/) (2022)
- [Locally Differentially Private Gradient Tracking for Distributed Online Learning over Directed Graphs](https://mlsanity.com/paper/2310.16105/) (2023)
- [FedEmb: A Vertical and Hybrid Federated Learning Algorithm using Network And Feature Embedding Aggregation](https://mlsanity.com/paper/2312.00102/) (2023)
- [Privacy-Preserving Distributed Optimization and Learning](https://mlsanity.com/paper/2403.00157/) (2024)
- [Accelerated Stochastic ExtraGradient: Mixing Hessian and Gradient Similarity to Reduce Communication in Distributed and Federated Learning](https://mlsanity.com/paper/2409.14280/) (2024)
- [Accelerated Methods with Compressed Communications for Distributed Optimization Problems under Data Similarity](https://mlsanity.com/paper/2412.16414/) (2024)
- [Differentially Private Equilibrium Finding in Polymatrix Games](https://mlsanity.com/paper/2503.09538/) (2025)

## Abstract (arXiv)

We study a class of distributed convex constrained optimization problems where a group of agents aim to minimize the sum of individual objective functions while each desires that any information about its objective function is kept private. We prove the impossibility of achieving differential privacy using strategies based on perturbing the inter-agent messages with noise when the underlying noise-free dynamics are asymptotically stable. This justifies our algorithmic solution based on the perturbation of individual functions with Laplace noise. To this end, we establish a general framework for differentially private handling of functional data. We further design post-processing steps that ensure the perturbed functions regain the smoothness and convexity properties of the original functions while preserving the differentially private guarantees of the functional perturbation step. This methodology allows us to use any distributed coordination algorithm to solve the optimization problem on the noisy functions. Finally, we explicitly bound the magnitude of the expected distance between the perturbed and true optimizers which leads to an upper bound on the privacy-accuracy trade-off curve. Simulations illustrate our results.