# Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework

arXiv: https://arxiv.org/abs/2004.13999 · HTML: https://mlsanity.com/paper/2004.13999/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2020.

## Built on by (most cited first, 10 of 10)

- [Mixture of Experts (MoE): A Big Data Perspective](https://mlsanity.com/paper/2501.16352/) (2025)
- [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)
- [Provable Privacy Advantages of Decentralized Federated Learning via Distributed Optimization](https://mlsanity.com/paper/2407.09324/) (2024)
- [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 Distributed Expectation Maximization for Gaussian Mixture Model using Subspace Perturbation](https://mlsanity.com/paper/2209.07833/) (2022)
- [LAGO: Few-shot Crosslingual Embedding Inversion Attacks via Language Similarity-Aware Graph Optimization](https://mlsanity.com/paper/2505.16008/) (2025)
- [AttentionX: Exploiting Consensus Discrepancy In Attention from A Distributed Optimization Perspective](https://mlsanity.com/paper/2409.04275/) (2024)
- [A Weighted Gradient Tracking Privacy-Preserving Method for Distributed Optimization](https://mlsanity.com/paper/2509.18134/) (2025)

## Abstract (arXiv)

As the modern world becomes increasingly digitized and interconnected, distributed signal processing has proven to be effective in processing its large volume of data. However, a main challenge limiting the broad use of distributed signal processing techniques is the issue of privacy in handling sensitive data. To address this privacy issue, we propose a novel yet general subspace perturbation method for privacy-preserving distributed optimization, which allows each node to obtain the desired solution while protecting its private data. In particular, we show that the dual variables introduced in each distributed optimizer will not converge in a certain subspace determined by the graph topology. Additionally, the optimization variable is ensured to converge to the desired solution, because it is orthogonal to this non-convergent subspace. We therefore propose to insert noise in the non-convergent subspace through the dual variable such that the private data are protected, and the accuracy of the desired solution is completely unaffected. Moreover, the proposed method is shown to be secure under two widely-used adversary models: passive and eavesdropping. Furthermore, we consider several distributed optimizers such as ADMM and PDMM to demonstrate the general applicability of the proposed method. Finally, we test the performance through a set of applications. Numerical tests indicate that the proposed method is superior to existing methods in terms of several parameters like estimated accuracy, privacy level, communication cost and convergence rate.