# Privacy Amplification for Federated Learning via User Sampling and Wireless Aggregation

arXiv: https://arxiv.org/abs/2103.01953 · HTML: https://mlsanity.com/paper/2103.01953/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 2 Mar 2021.

## Builds on (most cited first, 27 of 27)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Exploiting Unintended Feature Leakage in Collaborative Learning](https://mlsanity.com/paper/1805.04049/) (2018)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [Adaptive Federated Learning in Resource Constrained Edge Computing Systems](https://mlsanity.com/paper/1804.05271/) (2018)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [cpSGD: Communication-efficient and differentially-private distributed SGD](https://mlsanity.com/paper/1805.10559/) (2018)
- [Hierarchical Federated Learning Across Heterogeneous Cellular Networks](https://mlsanity.com/paper/1909.02362/) (2019)
- [Federated Learning for Edge Networks: Resource Optimization and Incentive Mechanism](https://mlsanity.com/paper/1911.05642/) (2019)
- [Privacy For Free: Wireless Federated Learning Via Uncoded Transmission With Adaptive Power Control](https://mlsanity.com/paper/2006.05459/) (2020)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [Federated Learning with Bayesian Differential Privacy](https://mlsanity.com/paper/1911.10071/) (2019)
- [Wireless Federated Learning with Local Differential Privacy](https://mlsanity.com/paper/2002.05151/) (2020)
- [Differential Privacy-enabled Federated Learning for Sensitive Health Data](https://mlsanity.com/paper/1910.02578/) (2019)
- [Energy-Efficient Radio Resource Allocation for Federated Edge Learning](https://mlsanity.com/paper/1907.06040/) (2019)
- [Encode, Shuffle, Analyze Privacy Revisited: Formalizations and Empirical Evaluation](https://mlsanity.com/paper/2001.03618/) (2020)
- [Privacy Amplification via Random Check-Ins](https://mlsanity.com/paper/2007.06605/) (2020)
- [Stochastic Gradient Descent with Biased but Consistent Gradient Estimators](https://mlsanity.com/paper/1807.11880/) (2018)
- [Private Wireless Federated Learning with Anonymous Over-the-Air Computation](https://mlsanity.com/paper/2011.08579/) (2020)
- [Local Differential Privacy for Evolving Data](https://mlsanity.com/paper/1802.07128/) (2018)
- [Efficient Federated Learning over Multiple Access Channel with Differential Privacy Constraints](https://mlsanity.com/paper/2005.07776/) (2020)

## Built on by (most cited first, 22 of 22)

- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Semi-Decentralized Federated Learning with Collaborative Relaying](https://mlsanity.com/paper/2205.10998/) (2022)
- [Trustworthy Federated Learning: Privacy, Security, and Beyond](https://mlsanity.com/paper/2411.01583/) (2024)
- [Over-the-Air Ensemble Inference with Model Privacy](https://mlsanity.com/paper/2202.03129/) (2022)
- [Over-the-Air Federated Learning and Optimization](https://mlsanity.com/paper/2310.10089/) (2023)
- [Robust Federated Learning with Connectivity Failures: A Semi-Decentralized Framework with Collaborative Relaying](https://mlsanity.com/paper/2202.11850/) (2022)
- [Differentially Private Federated Learning via Reconfigurable Intelligent Surface](https://mlsanity.com/paper/2203.17028/) (2022)
- [Social-Aware Clustered Federated Learning with Customized Privacy Preservation](https://mlsanity.com/paper/2212.13992/) (2022)
- [Communication and Energy Efficient Wireless Federated Learning with Intrinsic Privacy](https://mlsanity.com/paper/2304.07460/) (2023)
- [Differentially Private Over-the-Air Federated Learning Over MIMO Fading Channels](https://mlsanity.com/paper/2306.10982/) (2023)
- [Private Collaborative Edge Inference via Over-the-Air Computation](https://mlsanity.com/paper/2407.21151/) (2024)
- [Privacy Amplification via Random Participation in Federated Learning](https://mlsanity.com/paper/2205.01556/) (2022)
- [On Differential Privacy for Federated Learning in Wireless Systems with Multiple Base Stations](https://mlsanity.com/paper/2208.11848/) (2022)
- [Binary Federated Learning with Client-Level Differential Privacy](https://mlsanity.com/paper/2308.03320/) (2023)
- [Privacy Preserving Semi-Decentralized Mean Estimation over Intermittently-Connected Networks](https://mlsanity.com/paper/2406.03766/) (2024)
- [Differentially Private Wireless Federated Learning Using Orthogonal Sequences](https://mlsanity.com/paper/2306.08280/) (2023)
- [Collaborative Inference over Wireless Channels with Feature Differential Privacy](https://mlsanity.com/paper/2410.19917/) (2024)
- [Providing Differential Privacy for Federated Learning Over Wireless: A Cross-layer Framework](https://mlsanity.com/paper/2412.04408/) (2024)
- [Privacy-Preserving Quantized Federated Learning with Diverse Precision](https://mlsanity.com/paper/2507.00920/) (2025)
- [Communication-Learning Co-Design for Differentially Private Over-the-Air Federated Distillation](https://mlsanity.com/paper/2508.06557/) (2025)
- [Federated Learning with Enhanced Privacy via Model Splitting and Random Client Participation](https://mlsanity.com/paper/2509.25906/) (2025)

## Abstract (arXiv)

In this paper, we study the problem of federated learning over a wireless channel with user sampling, modeled by a Gaussian multiple access channel, subject to central and local differential privacy (DP/LDP) constraints. It has been shown that the superposition nature of the wireless channel provides a dual benefit of bandwidth efficient gradient aggregation, in conjunction with strong DP guarantees for the users. Specifically, the central DP privacy leakage has been shown to scale as O(1/K1/2), where K is the number of users. It has also been shown that user sampling coupled with orthogonal transmission can enhance the central DP privacy leakage with the same scaling behavior. In this work, we show that, by join incorporating both wireless aggregation and user sampling, one can obtain even stronger privacy guarantees. We propose a private wireless gradient aggregation scheme, which relies on independently randomized participation decisions by each user. The central DP leakage of our proposed scheme scales as O(1/K3/4). In addition, we show that LDP is also boosted by user sampling. We also present analysis for the convergence rate of the proposed scheme and study the tradeoffs between wireless resources, convergence, and privacy theoretically and empirically for two scenarios when the number of sampled participants are (a) known, or (b) unknown at the parameter server.