# Privacy-Aware Compression for Federated Learning Through Numerical Mechanism Design

arXiv: https://arxiv.org/abs/2211.03942 · HTML: https://mlsanity.com/paper/2211.03942/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 53 references that are in the map.
- First posted on arXiv 8 Nov 2022.

## Builds on (most cited first, 30 of 40)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [iDLG: Improved Deep Leakage from Gradients](https://mlsanity.com/paper/2001.02610/) (2020)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [See through Gradients: Image Batch Recovery via GradInversion](https://mlsanity.com/paper/2104.07586/) (2021)
- [Differentially Private Learning Needs Better Features (or Much More Data)](https://mlsanity.com/paper/2011.11660/) (2020)
- [Qsparse-local-SGD: Distributed SGD with Quantization, Sparsification, and Local Computations](https://mlsanity.com/paper/1906.02367/) (2019)
- [Federated Learning with Compression: Unified Analysis and Sharp Guarantees](https://mlsanity.com/paper/2007.01154/) (2020)
- [Reconstructing Training Data with Informed Adversaries](https://mlsanity.com/paper/2201.04845/) (2022)
- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2102.06387/) (2021)
- [Linear Convergence in Federated Learning: Tackling Client Heterogeneity and Sparse Gradients](https://mlsanity.com/paper/2102.07053/) (2021)
- [Gradient Inversion with Generative Image Prior](https://mlsanity.com/paper/2110.14962/) (2021)
- [Hypothesis Testing Interpretations and Renyi Differential Privacy](https://mlsanity.com/paper/1905.09982/) (2019)
- [Breaking the Communication-Privacy-Accuracy Trilemma](https://mlsanity.com/paper/2007.11707/) (2020)
- [The Skellam Mechanism for Differentially Private Federated Learning](https://mlsanity.com/paper/2110.04995/) (2021)
- [Bidirectional compression in heterogeneous settings for distributed or federated learning with partial participation: tight convergence guarantees](https://mlsanity.com/paper/2006.14591/) (2020)
- [Bounding Training Data Reconstruction in Private (Deep) Learning](https://mlsanity.com/paper/2201.12383/) (2022)
- [Optimal Gradient Compression for Distributed and Federated Learning](https://mlsanity.com/paper/2010.03246/) (2020)
- [The Fundamental Price of Secure Aggregation in Differentially Private Federated Learning](https://mlsanity.com/paper/2203.03761/) (2022)
- [Optimal Algorithms for Mean Estimation under Local Differential Privacy](https://mlsanity.com/paper/2205.02466/) (2022)
- [Stochastic-Sign SGD for Federated Learning with Theoretical Guarantees](https://mlsanity.com/paper/2002.10940/) (2020)

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

- [Universal Exact Compression of Differentially Private Mechanisms](https://mlsanity.com/paper/2405.20782/) (2024)
- [Exactly Minimax-Optimal Locally Differentially Private Sampling](https://mlsanity.com/paper/2410.22699/) (2024)
- [TernaryVote: Differentially Private, Communication Efficient, and Byzantine Resilient Distributed Optimization on Heterogeneous Data](https://mlsanity.com/paper/2402.10816/) (2024)
- [Privacy-Aware Randomized Quantization via Linear Programming](https://mlsanity.com/paper/2406.02599/) (2024)
- [On Using Secure Aggregation in Differentially Private Federated Learning with Multiple Local Steps](https://mlsanity.com/paper/2407.19286/) (2024)
- [PBM-VFL: Vertical Federated Learning with Feature and Sample Privacy](https://mlsanity.com/paper/2501.13916/) (2025)

## Abstract (arXiv)

In private federated learning (FL), a server aggregates differentially private updates from a large number of clients in order to train a machine learning model. The main challenge in this setting is balancing privacy with both classification accuracy of the learnt model as well as the number of bits communicated between the clients and server. Prior work has achieved a good trade-off by designing a privacy-aware compression mechanism, called the minimum variance unbiased (MVU) mechanism, that numerically solves an optimization problem to determine the parameters of the mechanism. This paper builds upon it by introducing a new interpolation procedure in the numerical design process that allows for a far more efficient privacy analysis. The result is the new Interpolated MVU mechanism that is more scalable, has a better privacy-utility trade-off, and provides SOTA results on communication-efficient private FL on a variety of datasets.