# Communication efficient privacy-preserving distributed optimization using adaptive differential quantization

arXiv: https://arxiv.org/abs/2105.14416 · HTML: https://mlsanity.com/paper/2105.14416/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 59 references that are in the map.
- First posted on arXiv 30 May 2021.

## Builds on (most cited first, 19 of 19)

- [Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimates](https://mlsanity.com/paper/1911.02151/) (2019)
- [Generalization Error Bounds for Noisy, Iterative Algorithms](https://mlsanity.com/paper/1801.04295/) (2018)
- [Differential Privacy as a Mutual Information Constraint](https://mlsanity.com/paper/1608.03677/) (2016)
- [Differentially Private Distributed Optimization](https://mlsanity.com/paper/1401.2596/) (2014)
- [Improving the Privacy and Accuracy of ADMM-Based Distributed Algorithms](https://mlsanity.com/paper/1806.02246/) (2018)
- [Information-Theoretic Bounds on the Generalization Error and Privacy Leakage in Federated Learning](https://mlsanity.com/paper/2005.02503/) (2020)
- [Distributed Optimization Using the Primal-Dual Method of Multipliers](https://mlsanity.com/paper/1702.00841/) (2017)
- [Differentially Private Distributed Constrained Optimization](https://mlsanity.com/paper/1411.4105/) (2014)
- [Differentially Private Distributed Convex Optimization via Functional Perturbation](https://mlsanity.com/paper/1512.00369/) (2015)
- [Convergence Rates with Inexact Non-expansive Operators](https://mlsanity.com/paper/1404.4837/) (2014)
- [Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework](https://mlsanity.com/paper/2004.13999/) (2020)
- [Derivation and Analysis of the Primal-Dual Method of Multipliers Based on Monotone Operator Theory](https://mlsanity.com/paper/1706.02654/) (2017)
- [Privacy-Preserving Distributed Processing: Metrics, Bounds, and Algorithms](https://mlsanity.com/paper/2009.01098/) (2020)
- [Recycled ADMM: Improve Privacy and Accuracy with Less Computation in Distributed Algorithms](https://mlsanity.com/paper/1810.03197/) (2018)
- [Quantized Consensus by the ADMM: Probabilistic versus Deterministic Quantizers](https://mlsanity.com/paper/1502.01053/) (2015)
- [Differentially Private Average Consensus: Obstructions, Trade-Offs, and Optimal Algorithm Design](https://mlsanity.com/paper/1512.09039/) (2015)
- [Privacy-preserving Average Consensus: Privacy Analysis and Optimal Algorithm Design](https://mlsanity.com/paper/1609.06368/) (2016)
- [Information-theoretic metrics for Local Differential Privacy protocols](https://mlsanity.com/paper/1910.07826/) (2019)
- [Statistical Privacy in Distributed Average Consensus on Bounded Real Inputs](https://mlsanity.com/paper/1903.09315/) (2019)

## Built on by (most cited first, 6 of 6)

- [Layered Randomized Quantization for Communication-Efficient and Privacy-Preserving Distributed Learning](https://mlsanity.com/paper/2312.07060/) (2023)
- [Provable Privacy Advantages of Decentralized Federated Learning via Distributed Optimization](https://mlsanity.com/paper/2407.09324/) (2024)
- [Killing Two Birds with One Stone: Quantization Achieves Privacy in Distributed Learning](https://mlsanity.com/paper/2304.13545/) (2023)
- [From Centralized to Decentralized Federated Learning: Theoretical Insights, Privacy Preservation, and Robustness Challenges](https://mlsanity.com/paper/2503.07505/) (2025)
- [Trustworthy Efficient Communication for Distributed Learning using LQ-SGD Algorithm](https://mlsanity.com/paper/2506.17974/) (2025)
- [Resource-Efficient Distributed Recursive Gaussian Processes](https://mlsanity.com/paper/2609.26979/) (2026)

## Abstract (arXiv)

Privacy issues and communication cost are both major concerns in distributed optimization. There is often a trade-off between them because the encryption methods required for privacy-preservation often incur expensive communication bandwidth. To address this issue, we, in this paper, propose a quantization-based approach to achieve both communication efficient and privacy-preserving solutions in the context of distributed optimization. By deploying an adaptive differential quantization scheme, we allow each node in the network to achieve its optimum solution with a low communication cost while keeping its private data unrevealed. Additionally, the proposed approach is general and can be applied in various distributed optimization methods, such as the primal-dual method of multipliers (PDMM) and the alternating direction method of multipliers (ADMM). Moveover, we consider two widely used adversary models: passive and eavesdropping. Finally, we investigate the properties of the proposed approach using different applications and demonstrate its superior performance in terms of several parameters including accuracy, privacy, and communication cost.