# Differential Privacy Analysis of Decentralized Gossip Averaging under Varying Threat Models

arXiv: https://arxiv.org/abs/2505.19969 · HTML: https://mlsanity.com/paper/2505.19969/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 54 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 30 of 33)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [A Hybrid Approach to Privacy-Preserving Federated Learning](https://mlsanity.com/paper/1812.03224/) (2018)
- [Private Stochastic Convex Optimization with Optimal Rates](https://mlsanity.com/paper/1908.09970/) (2019)
- [Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses](https://mlsanity.com/paper/2006.06914/) (2020)
- [Practical and Private (Deep) Learning without Sampling or Shuffling](https://mlsanity.com/paper/2103.00039/) (2021)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Asynchronous Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1710.06952/) (2017)
- [How to DP-fy ML: A Practical Guide to Machine Learning with Differential Privacy](https://mlsanity.com/paper/2303.00654/) (2023)
- [The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2102.06387/) (2021)
- [Optimal Accounting of Differential Privacy via Characteristic Function](https://mlsanity.com/paper/2106.08567/) (2021)
- [Improved Differential Privacy for SGD via Optimal Private Linear Operators on Adaptive Streams](https://mlsanity.com/paper/2202.08312/) (2022)
- [SNAP: A General Purpose Network Analysis and Graph Mining Library](https://mlsanity.com/paper/1606.07550/) (2016)
- [Personalized and Private Peer-to-Peer Machine Learning](https://mlsanity.com/paper/1705.08435/) (2017)
- [Walkman: A Communication-Efficient Random-Walk Algorithm for Decentralized Optimization](https://mlsanity.com/paper/1804.06568/) (2018)
- [Privacy Amplification by Decentralization](https://mlsanity.com/paper/2012.05326/) (2020)
- [Muffliato: Peer-to-Peer Privacy Amplification for Decentralized Optimization and Averaging](https://mlsanity.com/paper/2206.05091/) (2022)
- [Differentially Private Distributed Optimization](https://mlsanity.com/paper/1401.2596/) (2014)
- [On the (In)security of Peer-to-Peer Decentralized Machine Learning](https://mlsanity.com/paper/2205.08443/) (2022)
- [An Accurate, Scalable and Verifiable Protocol for Federated Differentially Private Averaging](https://mlsanity.com/paper/2006.07218/) (2020)
- [The Privacy Power of Correlated Noise in Decentralized Learning](https://mlsanity.com/paper/2405.01031/) (2024)
- [Privacy-preserving Decentralized Aggregation for Federated Learning](https://mlsanity.com/paper/2012.07183/) (2020)
- [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)
- [Differentially private and decentralized randomized power method](https://mlsanity.com/paper/2411.01931/) (2024)

## Built on by (most cited first, 2 of 2)

- [Unified Privacy Guarantees for Decentralized Learning via Matrix Factorization](https://mlsanity.com/paper/2510.17480/) (2025)
- [Reputation-driven Cooperation in Lattice-based Decentralized Federated Learning through Evolutionary Game Theory](https://mlsanity.com/paper/2608.01197/) (2026)

## Abstract (arXiv)

Achieving differential privacy (DP) guarantees in fully decentralized machine learning is challenging due to the absence of a central aggregator and varying trust assumptions among nodes. We present a framework for DP analysis of decentralized gossip-based averaging algorithms with additive node-level noise, from arbitrary views of nodes in a graph. We present an analytical framework based on a linear systems formulation that accurately characterizes privacy leakage between nodes. Our main contribution is showing that the DP guarantees are those of a Gaussian mechanism, where the growth of the squared sensitivity is asymptotically O(T), where T is the number of training rounds, similarly as in the case of central aggregation. As an application of the sensitivity analysis, we show that the excess risk of decentralized private learning for strongly convex losses is asymptotically similar as in centralized private learning.