# Byzantine-Robust Federated Learning with Optimal Statistical Rates and Privacy Guarantees

arXiv: https://arxiv.org/abs/2205.11765 · HTML: https://mlsanity.com/paper/2205.11765/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 82 references that are in the map.
- First posted on arXiv 24 May 2022.

## Builds on (most cited first, 30 of 47)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [How To Backdoor Federated Learning](https://mlsanity.com/paper/1807.00459/) (2018)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Local Model Poisoning Attacks to Byzantine-Robust Federated Learning](https://mlsanity.com/paper/1911.11815/) (2019)
- [Analyzing Federated Learning through an Adversarial Lens](https://mlsanity.com/paper/1811.12470/) (2018)
- [The Hidden Vulnerability of Distributed Learning in Byzantium](https://mlsanity.com/paper/1802.07927/) (2018)
- [Robust Aggregation for Federated Learning](https://mlsanity.com/paper/1912.13445/) (2019)
- [Attack of the Tails: Yes, You Really Can Backdoor Federated Learning](https://mlsanity.com/paper/2007.05084/) (2020)
- [Certified Defenses for Data Poisoning Attacks](https://mlsanity.com/paper/1706.03691/) (2017)
- [Can You Really Backdoor Federated Learning?](https://mlsanity.com/paper/1911.07963/) (2019)
- [Beyond Inferring Class Representatives: User-Level Privacy Leakage From Federated Learning](https://mlsanity.com/paper/1812.00535/) (2018)
- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Mitigating Sybils in Federated Learning Poisoning](https://mlsanity.com/paper/1808.04866/) (2018)
- [Fall of Empires: Breaking Byzantine-tolerant SGD by Inner Product Manipulation](https://mlsanity.com/paper/1903.03936/) (2019)
- [Learning from History for Byzantine Robust Optimization](https://mlsanity.com/paper/2012.10333/) (2020)
- [Agnostic Estimation of Mean and Covariance](https://mlsanity.com/paper/1604.06968/) (2016)
- [Byzantine-Robust Learning on Heterogeneous Datasets via Bucketing](https://mlsanity.com/paper/2006.09365/) (2020)
- [Sever: A Robust Meta-Algorithm for Stochastic Optimization](https://mlsanity.com/paper/1803.02815/) (2018)
- [Feature Inference Attack on Model Predictions in Vertical Federated Learning](https://mlsanity.com/paper/2010.10152/) (2020)
- [Byzantine-Resilient Secure Federated Learning](https://mlsanity.com/paper/2007.11115/) (2020)
- [Being Robust (in High Dimensions) Can Be Practical](https://mlsanity.com/paper/1703.00893/) (2017)
- [Byzantine Stochastic Gradient Descent](https://mlsanity.com/paper/1803.08917/) (2018)
- [Efficient Algorithms and Lower Bounds for Robust Linear Regression](https://mlsanity.com/paper/1806.00040/) (2018)
- [DRACO: Byzantine-resilient Distributed Training via Redundant Gradients](https://mlsanity.com/paper/1803.09877/) (2018)
- [Data Poisoning Attacks on Federated Machine Learning](https://mlsanity.com/paper/2004.10020/) (2020)
- [Byzantine-Resilient Non-Convex Stochastic Gradient Descent](https://mlsanity.com/paper/2012.14368/) (2020)
- [Outlier Robust Mean Estimation with Subgaussian Rates via Stability](https://mlsanity.com/paper/2007.15618/) (2020)

## Built on by (most cited first, 30 of 30)

- [Practical Differentially Private and Byzantine-resilient Federated Learning](https://mlsanity.com/paper/2304.09762/) (2023)
- [Provably Unlearnable Data Examples](https://mlsanity.com/paper/2405.03316/) (2024)
- [A Huber Loss Minimization Approach to Byzantine Robust Federated Learning](https://mlsanity.com/paper/2308.12581/) (2023)
- [Byzantine-Robust Federated Learning: Impact of Client Subsampling and Local Updates](https://mlsanity.com/paper/2402.12780/) (2024)
- [High Dimensional Distributed Gradient Descent with Arbitrary Number of Byzantine Attackers](https://mlsanity.com/paper/2307.13352/) (2023)
- [S2FGL: Spatial Spectral Federated Graph Learning](https://mlsanity.com/paper/2507.02409/) (2025)
- [FedSV: Byzantine-Robust Federated Learning via Shapley Value](https://mlsanity.com/paper/2502.17526/) (2025)
- [MixTailor: Mixed Gradient Aggregation for Robust Learning Against Tailored Attacks](https://mlsanity.com/paper/2207.07941/) (2022)
- [On the Byzantine-Resilience of Distillation-Based Federated Learning](https://mlsanity.com/paper/2402.12265/) (2024)
- [Fine-Tuning Personalization in Federated Learning to Mitigate Adversarial Clients](https://mlsanity.com/paper/2409.20329/) (2024)
- [Near-Optimal Resilient Aggregation Rules for Distributed Learning Using 1-Center and 1-Mean Clustering with Outliers](https://mlsanity.com/paper/2312.12835/) (2023)
- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [Review of Mathematical Optimization in Federated Learning](https://mlsanity.com/paper/2412.01630/) (2024)
- [Delayed Momentum Aggregation: Communication-efficient Byzantine-robust Federated Learning with Partial Participation](https://mlsanity.com/paper/2509.02970/) (2025)
- [WW-FL: Secure and Private Large-Scale Federated Learning](https://mlsanity.com/paper/2302.09904/) (2023)
- [TernaryVote: Differentially Private, Communication Efficient, and Byzantine Resilient Distributed Optimization on Heterogeneous Data](https://mlsanity.com/paper/2402.10816/) (2024)
- [Tight Stability Bounds for Robust Distributed Learning: Byzantine Failures Hurt Generalization More than Data Poisoning](https://mlsanity.com/paper/2506.18020/) (2025)
- [Exploring the Robustness of Decentralized Training for Large Language Models](https://mlsanity.com/paper/2312.00843/) (2023)
- [Attacking Byzantine Robust Aggregation in High Dimensions](https://mlsanity.com/paper/2312.14461/) (2023)
- [Harnessing the Power of Federated Learning in Federated Contextual Bandits](https://mlsanity.com/paper/2312.16341/) (2023)
- [Distributionally Robust Federated Learning with Outlier Resilience](https://mlsanity.com/paper/2509.24462/) (2025)
- [A Byzantine-Robust Federated Learning with Nesterov Momentum](https://mlsanity.com/paper/2511.02657/) (2025)
- [When More Data Doesn't Help: Limits of Adaptation in Multitask Learning](https://mlsanity.com/paper/2601.20774/) (2026)
- [mathsfVISTA: Decentralized Machine Learning in Adversary Dominated Environments](https://mlsanity.com/paper/2605.07841/) (2026)
- [On the Gradient Heterogeneity Dynamics of Adversarially Robust Federated Regression](https://mlsanity.com/paper/2609.25705/) (2026)
- [Byzantine-Robust Clustered Federated Learning](https://mlsanity.com/paper/2306.00638/) (2023)
- [FedVSR: Towards Model-Agnostic Federated Learning in Video Super-Resolution](https://mlsanity.com/paper/2503.13745/) (2025)
- [Financial Data Analysis with Robust Federated Logistic Regression](https://mlsanity.com/paper/2504.20250/) (2025)
- [Online Security Learning in Cooperative Multi-Agent Systems under Hidden Byzantine Attacks](https://mlsanity.com/paper/2608.06520/) (2026)
- [Robustifying Asynchronous SGD via Soft Throttling](https://mlsanity.com/paper/2609.39357/) (2026)

## Abstract (arXiv)

We propose Byzantine-robust federated learning protocols with nearly optimal statistical rates. In contrast to prior work, our proposed protocols improve the dimension dependence and achieve a tight statistical rate in terms of all the parameters for strongly convex losses. We benchmark against competing protocols and show the empirical superiority of the proposed protocols. Finally, we remark that our protocols with bucketing can be naturally combined with privacy-guaranteeing procedures to introduce security against a semi-honest server. The code for evaluation is provided in https://github.com/wanglun1996/secure-robust-federated-learning.