# Differentially Private Distributed Constrained Optimization

arXiv: https://arxiv.org/abs/1411.4105 · HTML: https://mlsanity.com/paper/1411.4105/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2014.

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

- [Trustworthy AI: From Principles to Practices](https://mlsanity.com/paper/2110.01167/) (2021)
- [Communication efficient privacy-preserving distributed optimization using adaptive differential quantization](https://mlsanity.com/paper/2105.14416/) (2021)
- [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)
- [Enhancing Privacy in Federated Learning through Local Training](https://mlsanity.com/paper/2403.17572/) (2024)
- [Differential Privacy via Distributionally Robust Optimization](https://mlsanity.com/paper/2304.12681/) (2023)
- [Privacy-Preserving Distributed Optimization and Learning](https://mlsanity.com/paper/2403.00157/) (2024)
- [Locally Differentially Private Distributed Online Learning with Guaranteed Optimality](https://mlsanity.com/paper/2306.14094/) (2023)
- [Realistic Differentially-Private Transmission Power Flow Data Release](https://mlsanity.com/paper/2103.14036/) (2021)
- [Privacy-Preserving Matrix Factorization for Recommendation Systems using Gaussian Mechanism](https://mlsanity.com/paper/2304.09096/) (2023)
- [Near-optimal Differentially Private Client Selection in Federated Settings](https://mlsanity.com/paper/2310.09370/) (2023)

## Abstract (arXiv)

Many resource allocation problems can be formulated as an optimization problem whose constraints contain sensitive information about participating users. This paper concerns solving this kind of optimization problem in a distributed manner while protecting the privacy of user information. Without privacy considerations, existing distributed algorithms normally consist in a central entity computing and broadcasting certain public coordination signals to participating users. However, the coordination signals often depend on user information, so that an adversary who has access to the coordination signals can potentially decode information on individual users and put user privacy at risk. We present a distributed optimization algorithm that preserves differential privacy, which is a strong notion that guarantees user privacy regardless of any auxiliary information an adversary may have. The algorithm achieves privacy by perturbing the public signals with additive noise, whose magnitude is determined by the sensitivity of the projection operation onto user-specified constraints. By viewing the differentially private algorithm as an implementation of stochastic gradient descent, we are able to derive a bound for the suboptimality of the algorithm. We illustrate the implementation of our algorithm via a case study of electric vehicle charging. Specifically, we derive the sensitivity and present numerical simulations for the algorithm. Through numerical simulations, we are able to investigate various aspects of the algorithm when being used in practice, including the choice of step size, number of iterations, and the trade-off between privacy level and suboptimality.