# A Huber Loss Minimization Approach to Byzantine Robust Federated Learning

arXiv: https://arxiv.org/abs/2308.12581 · HTML: https://mlsanity.com/paper/2308.12581/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 33 references that are in the map.
- First posted on arXiv 24 Aug 2023.

## Builds on (most cited first, 18 of 18)

- [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)
- [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)
- [Local Model Poisoning Attacks to Byzantine-Robust Federated Learning](https://mlsanity.com/paper/1911.11815/) (2019)
- [Robust Aggregation for Federated Learning](https://mlsanity.com/paper/1912.13445/) (2019)
- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [RSA: Byzantine-Robust Stochastic Aggregation Methods for Distributed Learning from Heterogeneous Datasets](https://mlsanity.com/paper/1811.03761/) (2018)
- [Robust Federated Learning in a Heterogeneous Environment](https://mlsanity.com/paper/1906.06629/) (2019)
- [Being Robust (in High Dimensions) Can Be Practical](https://mlsanity.com/paper/1703.00893/) (2017)
- [Federated Variance-Reduced Stochastic Gradient Descent with Robustness to Byzantine Attacks](https://mlsanity.com/paper/1912.12716/) (2019)
- [Geometric Median in Nearly Linear Time](https://mlsanity.com/paper/1606.05225/) (2016)
- [Byzantine-Robust Federated Learning with Optimal Statistical Rates and Privacy Guarantees](https://mlsanity.com/paper/2205.11765/) (2022)
- [List-Decodable Mean Estimation in Nearly-PCA Time](https://mlsanity.com/paper/2011.09973/) (2020)
- [How Hard Is Robust Mean Estimation?](https://mlsanity.com/paper/1903.07870/) (2019)
- [Robust Nonparametric Regression under Poisoning Attack](https://mlsanity.com/paper/2305.16771/) (2023)
- [High Dimensional Distributed Gradient Descent with Arbitrary Number of Byzantine Attackers](https://mlsanity.com/paper/2307.13352/) (2023)
- [Securing Distributed Gradient Descent in High Dimensional Statistical Learning](https://mlsanity.com/paper/1804.10140/) (2018)

## Built on by (most cited first, 16 of 16)

- [Threats and Defenses in Federated Learning Life Cycle: A Comprehensive Survey and Challenges](https://mlsanity.com/paper/2407.06754/) (2024)
- [A Huber Loss Minimization Approach to Mean Estimation under User-level Differential Privacy](https://mlsanity.com/paper/2405.13453/) (2024)
- [Federated Learning Resilient to Byzantine Attacks and Data Heterogeneity](https://mlsanity.com/paper/2403.13374/) (2024)
- [Learning with User-Level Local Differential Privacy](https://mlsanity.com/paper/2405.17079/) (2024)
- [Developing Cryptocurrency Trading Strategy Based on Autoencoder-CNN-GANs Algorithms](https://mlsanity.com/paper/2412.18202/) (2024)
- [SketchAgent: Generating Structured Diagrams from Hand-Drawn Sketches](https://mlsanity.com/paper/2508.01237/) (2025)
- [Efficient Federated Learning against Byzantine Attacks and Data Heterogeneity via Aggregating Normalized Gradients](https://mlsanity.com/paper/2408.09539/) (2024)
- [Differential Private Stochastic Optimization with Heavy-tailed Data: Towards Optimal Rates](https://mlsanity.com/paper/2408.09891/) (2024)
- [FedSECA: Sign Election and Coordinate-wise Aggregation of Gradients for Byzantine Tolerant Federated Learning](https://mlsanity.com/paper/2411.03861/) (2024)
- [Coded Robust Aggregation for Distributed Learning under Byzantine Attacks](https://mlsanity.com/paper/2506.01989/) (2025)
- [FedIDM: Achieving Fast and Stable Convergence in Byzantine Federated Learning through Iterative Distribution Matching](https://mlsanity.com/paper/2604.15115/) (2026)
- [Byzantine-Robust Distributed Sparse Learning Revisited](https://mlsanity.com/paper/2605.13283/) (2026)
- [Dimensionality Reduction for Robust Federated Learning: A Theoretical Analysis and Convergence Guarantee](https://mlsanity.com/paper/2605.28335/) (2026)
- [Enhanced Byzantine-Robust Federated Learning Via Truncated-Quadratic Loss for Heterogeneous Data](https://mlsanity.com/paper/2607.10970/) (2026)
- [Median-of-Means as an Extremal Convex Estimator and a Nonconvex Route to the Trimmed Oracle](https://mlsanity.com/paper/2609.01689/) (2026)
- [Upholding Robustness in Federated Learning: Trends, Emerging Strategies, and Research Opportunities](https://mlsanity.com/paper/2609.28722/) (2026)

## Abstract (arXiv)

Federated learning systems are susceptible to adversarial attacks. To combat this, we introduce a novel aggregator based on Huber loss minimization, and provide a comprehensive theoretical analysis. Under independent and identically distributed (i.i.d) assumption, our approach has several advantages compared to existing methods. Firstly, it has optimal dependence on ε, which stands for the ratio of attacked clients. Secondly, our approach does not need precise knowledge of ε. Thirdly, it allows different clients to have unequal data sizes. We then broaden our analysis to include non-i.i.d data, such that clients have slightly different distributions.