# BRIDGE: Byzantine-resilient Decentralized Gradient Descent

arXiv: https://arxiv.org/abs/1908.08098 · HTML: https://mlsanity.com/paper/1908.08098/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Aug 2019.

## Built on by (most cited first, 30 of 45)

- [Byzantine-Robust Decentralized Learning via ClippedGossip](https://mlsanity.com/paper/2202.01545/) (2022)
- [Robust Training in High Dimensions via Block Coordinate Geometric Median Descent](https://mlsanity.com/paper/2106.08882/) (2021)
- [BROADCAST: Reducing Both Stochastic and Compression Noise to Robustify Communication-Efficient Federated Learning](https://mlsanity.com/paper/2104.06685/) (2021)
- [Secure Distributed Training at Scale](https://mlsanity.com/paper/2106.11257/) (2021)
- [Robust Collaborative Learning with Linear Gradient Overhead](https://mlsanity.com/paper/2209.10931/) (2022)
- [Backdoor Attacks in Peer-to-Peer Federated Learning](https://mlsanity.com/paper/2301.09732/) (2023)
- [On the Tradeoff between Privacy Preservation and Byzantine-Robustness in Decentralized Learning](https://mlsanity.com/paper/2308.14606/) (2023)
- [Unified Breakdown Analysis for Byzantine Robust Gossip](https://mlsanity.com/paper/2410.10418/) (2024)
- [Can Decentralized Learning be more robust than Federated Learning?](https://mlsanity.com/paper/2303.03829/) (2023)
- [Bristle: Decentralized Federated Learning in Byzantine, Non-i.i.d. Environments](https://mlsanity.com/paper/2110.11006/) (2021)
- [Privacy-Preserving Aggregation for Decentralized Learning with Byzantine-Robustness](https://mlsanity.com/paper/2404.17970/) (2024)
- [Generalization Error Matters in Decentralized Learning Under Byzantine Attacks](https://mlsanity.com/paper/2407.08632/) (2024)
- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [SPIRT: A Fault-Tolerant and Reliable Peer-to-Peer Serverless ML Training Architecture](https://mlsanity.com/paper/2309.14148/) (2023)
- [Byzantine-Resilient Decentralized Multi-Armed Bandits](https://mlsanity.com/paper/2310.07320/) (2023)
- [Resilience in Online Federated Learning: Mitigating Model-Poisoning Attacks via Partial Sharing](https://mlsanity.com/paper/2403.13108/) (2024)
- [Review of Mathematical Optimization in Federated Learning](https://mlsanity.com/paper/2412.01630/) (2024)
- [Robust and Efficient Aggregation for Distributed Learning](https://mlsanity.com/paper/2204.00586/) (2022)
- [Variance Reduction is an Antidote to Byzantines: Better Rates, Weaker Assumptions and Communication Compression as a Cherry on the Top](https://mlsanity.com/paper/2206.00529/) (2022)
- [Byzantine-Robust Decentralized Stochastic Optimization with Stochastic Gradient Noise-Independent Learning Error](https://mlsanity.com/paper/2308.05292/) (2023)
- [Competitive Advantage Attacks to Decentralized Federated Learning](https://mlsanity.com/paper/2310.13862/) (2023)
- [Learning to Help in Multi-Class Settings](https://mlsanity.com/paper/2501.13810/) (2025)
- [Stochastic Alternating Direction Method of Multipliers for Byzantine-Robust Distributed Learning](https://mlsanity.com/paper/2106.06891/) (2021)
- [Attacks on Robust Distributed Learning Schemes via Sensitivity Curve Maximization](https://mlsanity.com/paper/2304.14024/) (2023)
- [Exploring the Robustness of Decentralized Training for Large Language Models](https://mlsanity.com/paper/2312.00843/) (2023)
- [Mitigating Data Injection Attacks on Federated Learning](https://mlsanity.com/paper/2312.02102/) (2023)
- [On the Conflict of Robustness and Learning in Collaborative Machine Learning](https://mlsanity.com/paper/2402.13700/) (2024)
- [Byzantine-Robust Gossip: Insights from a Dual Approach](https://mlsanity.com/paper/2405.03449/) (2024)
- [Generalization Error Analysis for Attack-Free and Byzantine-Resilient Decentralized Learning with Data Heterogeneity](https://mlsanity.com/paper/2506.09438/) (2025)
- [Your Neighbors Know: Leveraging Local Neighborhoods for Backdoor Detection in Decentralized Learning](https://mlsanity.com/paper/2605.19969/) (2026)

## Abstract (arXiv)

Machine learning has begun to play a central role in many applications. A multitude of these applications typically also involve datasets that are distributed across multiple computing devices/machines due to either design constraints (e.g., multiagent systems) or computational/privacy reasons (e.g., learning on smartphone data). Such applications often require the learning tasks to be carried out in a decentralized fashion, in which there is no central server that is directly connected to all nodes. In real-world decentralized settings, nodes are prone to undetected failures due to malfunctioning equipment, cyberattacks, etc., which are likely to crash non-robust learning algorithms. The focus of this paper is on robustification of decentralized learning in the presence of nodes that have undergone Byzantine failures. The Byzantine failure model allows faulty nodes to arbitrarily deviate from their intended behaviors, thereby ensuring designs of the most robust of algorithms. But the study of Byzantine resilience within decentralized learning, in contrast to distributed learning, is still in its infancy. In particular, existing Byzantine-resilient decentralized learning methods either do not scale well to large-scale machine learning models, or they lack statistical convergence guarantees that help characterize their generalization errors. In this paper, a scalable, Byzantine-resilient decentralized machine learning framework termed Byzantine-resilient decentralized gradient descent (BRIDGE) is introduced. Algorithmic and statistical convergence guarantees for one variant of BRIDGE are also provided in the paper for both strongly convex problems and a class of nonconvex problems. In addition, large-scale decentralized learning experiments are used to establish that the BRIDGE framework is scalable and it delivers competitive results for Byzantine-resilient convex and nonconvex learning.