# Byzantine-Robust Federated Learning: Impact of Client Subsampling and Local Updates

arXiv: https://arxiv.org/abs/2402.12780 · HTML: https://mlsanity.com/paper/2402.12780/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 25 of 25)

- [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)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Robust Aggregation for Federated Learning](https://mlsanity.com/paper/1912.13445/) (2019)
- [A Little Is Enough: Circumventing Defenses For Distributed Learning](https://mlsanity.com/paper/1902.06156/) (2019)
- [Achieving Linear Speedup with Partial Worker Participation in Non-IID Federated Learning](https://mlsanity.com/paper/2101.11203/) (2021)
- [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)
- [Byzantine-Robust Learning on Heterogeneous Datasets via Bucketing](https://mlsanity.com/paper/2006.09365/) (2020)
- [Generalized Byzantine-tolerant SGD](https://mlsanity.com/paper/1802.10116/) (2018)
- [Fixing by Mixing: A Recipe for Optimal Byzantine ML under Heterogeneity](https://mlsanity.com/paper/2302.01772/) (2023)
- [FedVARP: Tackling the Variance Due to Partial Client Participation in Federated Learning](https://mlsanity.com/paper/2207.14130/) (2022)
- [Byzantine Machine Learning Made Easy by Resilient Averaging of Momentums](https://mlsanity.com/paper/2205.12173/) (2022)
- [Byzantine-Resilient Non-Convex Stochastic Gradient Descent](https://mlsanity.com/paper/2012.14368/) (2020)
- [Byzantine-Robust Federated Learning with Optimal Statistical Rates and Privacy Guarantees](https://mlsanity.com/paper/2205.11765/) (2022)
- [Approximate Byzantine Fault-Tolerance in Distributed Optimization](https://mlsanity.com/paper/2101.09337/) (2021)
- [Byzantine-Resilient High-Dimensional Federated Learning](https://mlsanity.com/paper/2006.13041/) (2020)
- [Personalization Improves Privacy-Accuracy Tradeoffs in Federated Learning](https://mlsanity.com/paper/2202.05318/) (2022)
- [Robust Training in High Dimensions via Block Coordinate Geometric Median Descent](https://mlsanity.com/paper/2106.08882/) (2021)
- [On the Strategyproofness of the Geometric Median](https://mlsanity.com/paper/2106.02394/) (2021)
- [Byzantine Fault-Tolerance in Federated Local SGD under 2f-Redundancy](https://mlsanity.com/paper/2108.11769/) (2021)

## Built on by (most cited first, 14 of 14)

- [ByzFL: Research Framework for Robust Federated Learning](https://mlsanity.com/paper/2505.24802/) (2025)
- [Bant: Byzantine Antidote via Trial Function and Trust Scores](https://mlsanity.com/paper/2505.07614/) (2025)
- [FedGreed: A Byzantine-Robust Loss-Based Aggregation Method for Federated Learning](https://mlsanity.com/paper/2508.18060/) (2025)
- [Delayed Momentum Aggregation: Communication-efficient Byzantine-robust Federated Learning with Partial Participation](https://mlsanity.com/paper/2509.02970/) (2025)
- [Robust Federated Learning under Adversarial Attacks via Loss-Based Client Clustering](https://mlsanity.com/paper/2508.12672/) (2025)
- [Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Framework](https://mlsanity.com/paper/2502.00846/) (2025)
- [On the Gradient Heterogeneity Dynamics of Adversarially Robust Federated Regression](https://mlsanity.com/paper/2609.25705/) (2026)
- [Analysis of Asynchronous Federated Learning: Unraveling the Interactions between Gradient Compression, Delay, and Data Heterogeneity](https://mlsanity.com/paper/2504.19903/) (2025)
- [Trade-off in Estimating the Number of Byzantine Clients in Federated Learning](https://mlsanity.com/paper/2510.04432/) (2025)
- [Robust and Efficient Collaborative Learning](https://mlsanity.com/paper/2510.08311/) (2025)
- [Revealing the influence of participant failures on model quality in cross-silo Federated Learning](https://mlsanity.com/paper/2603.25289/) (2026)
- [Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization](https://mlsanity.com/paper/2608.06563/) (2026)
- [FedVAR: Prototype-Aligned Federated Framework for Video Anomaly Recognition](https://mlsanity.com/paper/2608.06876/) (2026)
- [Robustifying Asynchronous SGD via Soft Throttling](https://mlsanity.com/paper/2609.39357/) (2026)

## Abstract (arXiv)

The possibility of adversarial (a.k.a., em Byzantine) clients makes federated learning (FL) prone to arbitrary manipulation. The natural approach to robustify FL against adversarial clients is to replace the simple averaging operation at the server in the standard mathsfFedAvg algorithm by a robust averaging rule. While a significant amount of work has been devoted to studying the convergence of federated em robust averaging (which we denote by mathsfFedRo), prior work has largely ignored the impact of em client subsampling and em local steps, two fundamental FL characteristics. While client subsampling increases the effective fraction of Byzantine clients, local steps increase the drift between the local updates computed by honest (i.e., non-Byzantine) clients. Consequently, a careless deployment of mathsfFedRo could yield poor performance. We validate this observation by presenting an in-depth analysis of mathsfFedRo tightly analyzing the impact of client subsampling and local steps. Specifically, we present a sufficient condition on client subsampling for nearly-optimal convergence of mathsfFedRo (for smooth non-convex loss). Also, we show that the rate of improvement in learning accuracy em diminishes with respect to the number of clients subsampled, as soon as the sample size exceeds a threshold value. Interestingly, we also observe that under a careful choice of step-sizes, the learning error due to Byzantine clients decreases with the number of local steps. We validate our theory by experiments on the FEMNIST and CIFAR-10 image classification tasks.