# Muffliato: Peer-to-Peer Privacy Amplification for Decentralized Optimization and Averaging

arXiv: https://arxiv.org/abs/2206.05091 · HTML: https://mlsanity.com/paper/2206.05091/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 68 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 29 of 29)

- [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)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (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)
- [Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication](https://mlsanity.com/paper/1902.00340/) (2019)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Differentially Private Empirical Risk Minimization Revisited: Faster and More General](https://mlsanity.com/paper/1802.05251/) (2018)
- [Network Topology and Communication-Computation Tradeoffs in Decentralized Optimization](https://mlsanity.com/paper/1709.08765/) (2017)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Privacy Amplification by Iteration](https://mlsanity.com/paper/1808.06651/) (2018)
- [Hiding Among the Clones: A Simple and Nearly Optimal Analysis of Privacy Amplification by Shuffling](https://mlsanity.com/paper/2012.12803/) (2020)
- [Optimal algorithms for smooth and strongly convex distributed optimization in networks](https://mlsanity.com/paper/1702.08704/) (2017)
- [Individual Privacy Accounting via a Renyi Filter](https://mlsanity.com/paper/2008.11193/) (2020)
- [Exponential Graph is Provably Efficient for Decentralized Deep Training](https://mlsanity.com/paper/2110.13363/) (2021)
- [Personalized and Private Peer-to-Peer Machine Learning](https://mlsanity.com/paper/1705.08435/) (2017)
- [Privacy Amplification by Decentralization](https://mlsanity.com/paper/2012.05326/) (2020)
- [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)
- [Empirical Risk Minimization in Non-interactive Local Differential Privacy: Efficiency and High Dimensional Case](https://mlsanity.com/paper/1802.04085/) (2018)
- [Lower Bounds and Optimal Algorithms for Smooth and Strongly Convex Decentralized Optimization Over Time-Varying Networks](https://mlsanity.com/paper/2106.04469/) (2021)
- [Accelerated Gossip in Networks of Given Dimension using Jacobi Polynomial Iterations](https://mlsanity.com/paper/1805.08531/) (2018)
- [Pure Differentially Private Summation from Anonymous Messages](https://mlsanity.com/paper/2002.01919/) (2020)
- [Collect at Once, Use Effectively: Making Non-interactive Locally Private Learning Possible](https://mlsanity.com/paper/1706.03316/) (2017)
- [Linear Convergence of Primal-Dual Gradient Methods and their Performance in Distributed Optimization](https://mlsanity.com/paper/1904.01196/) (2019)
- [An Accelerated Decentralized Stochastic Proximal Algorithm for Finite Sums](https://mlsanity.com/paper/1905.11394/) (2019)
- [Differentially Private Summation with Multi-Message Shuffling](https://mlsanity.com/paper/1906.09116/) (2019)
- [Asynchrony and Acceleration in Gossip Algorithms](https://mlsanity.com/paper/2011.02379/) (2020)

## Built on by (most cited first, 27 of 27)

- [Stochastic Gradient Descent under Markovian Sampling Schemes](https://mlsanity.com/paper/2302.14428/) (2023)
- [The Privacy Power of Correlated Noise in Decentralized Learning](https://mlsanity.com/paper/2405.01031/) (2024)
- [Beyond Exponential Graph: Communication-Efficient Topologies for Decentralized Learning via Finite-time Convergence](https://mlsanity.com/paper/2305.11420/) (2023)
- [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)
- [From Noisy Fixed-Point Iterations to Private ADMM for Centralized and Federated Learning](https://mlsanity.com/paper/2302.12559/) (2023)
- [Topology-Based Reconstruction Prevention for Decentralised Learning](https://mlsanity.com/paper/2312.05248/) (2023)
- [Low-Cost Privacy-Preserving Decentralized Learning](https://mlsanity.com/paper/2403.11795/) (2024)
- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [Mitigating Privacy-Utility Trade-off in Decentralized Federated Learning via f-Differential Privacy](https://mlsanity.com/paper/2510.19934/) (2025)
- [Communication-Efficient Secure Aggregation in Decentralized Learning](https://mlsanity.com/paper/2405.07708/) (2024)
- [PDSL: Privacy-Preserved Decentralized Stochastic Learning with Heterogeneous Data Distribution](https://mlsanity.com/paper/2503.23726/) (2025)
- [Differential Privacy Analysis of Decentralized Gossip Averaging under Varying Threat Models](https://mlsanity.com/paper/2505.19969/) (2025)
- [Unified Privacy Guarantees for Decentralized Learning via Matrix Factorization](https://mlsanity.com/paper/2510.17480/) (2025)
- [Generalizing Differentially Private Decentralized Deep Learning with Multi-Agent Consensus](https://mlsanity.com/paper/2306.13892/) (2023)
- [Fair Decentralized Learning](https://mlsanity.com/paper/2410.02541/) (2024)
- [Fedivertex: a Graph Dataset based on Decentralized Social Networks for Trustworthy Machine Learning](https://mlsanity.com/paper/2505.20882/) (2025)
- [Your Neighbors Know: Leveraging Local Neighborhoods for Backdoor Detection in Decentralized Learning](https://mlsanity.com/paper/2605.19969/) (2026)
- [Communication-Efficient and Privacy-Preserving Decentralized Meta-Learning](https://mlsanity.com/paper/2406.13183/) (2024)
- [Differentially Private Equilibrium Finding in Polymatrix Games](https://mlsanity.com/paper/2503.09538/) (2025)
- [GRANITE : a Byzantine-Resilient Dynamic Gossip Learning Framework](https://mlsanity.com/paper/2504.17471/) (2025)
- [Dropout-Robust Mechanisms for Differentially Private and Fully Decentralized Mean Estimation](https://mlsanity.com/paper/2506.03746/) (2025)
- [Topology-Aware Differential Privacy in Hierarchical Federated Learning](https://mlsanity.com/paper/2506.19260/) (2025)
- [Enhancing Privacy in Decentralized Min-Max Optimization: A Differentially Private Approach](https://mlsanity.com/paper/2508.07505/) (2025)
- [DPDL: Towards Differential Privacy Preservation in Decentralized Stochastic Learning on Non-IID Data](https://mlsanity.com/paper/2606.04399/) (2026)
- [Private Decentralized Optimization with Noise Reduction and Bias Correction](https://mlsanity.com/paper/2609.27658/) (2026)
- [SPADE-DFL: Communication-Efficient Decentralized Federated Learning via Derivative-Free Linearized ADMM](https://mlsanity.com/paper/2609.29446/) (2026)

## Abstract (arXiv)

Decentralized optimization is increasingly popular in machine learning for its scalability and efficiency. Intuitively, it should also provide better privacy guarantees, as nodes only observe the messages sent by their neighbors in the network graph. But formalizing and quantifying this gain is challenging: existing results are typically limited to Local Differential Privacy (LDP) guarantees that overlook the advantages of decentralization. In this work, we introduce pairwise network differential privacy, a relaxation of LDP that captures the fact that the privacy leakage from a node u to a node v may depend on their relative position in the graph. We then analyze the combination of local noise injection with (simple or randomized) gossip averaging protocols on fixed and random communication graphs. We also derive a differentially private decentralized optimization algorithm that alternates between local gradient descent steps and gossip averaging. Our results show that our algorithms amplify privacy guarantees as a function of the distance between nodes in the graph, matching the privacy-utility trade-off of the trusted curator, up to factors that explicitly depend on the graph topology. Finally, we illustrate our privacy gains with experiments on synthetic and real-world datasets.