# Decentralized Adversarial Training over Graphs

arXiv: https://arxiv.org/abs/2303.13326 · HTML: https://mlsanity.com/paper/2303.13326/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 80 references that are in the map.
- First posted on arXiv 23 Mar 2023.

## Builds on (most cited first, 30 of 51)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [Adversarial Examples for Evaluating Reading Comprehension Systems](https://mlsanity.com/paper/1707.07328/) (2017)
- [Decision-Based Adversarial Attacks: Reliable Attacks Against Black-Box Machine Learning Models](https://mlsanity.com/paper/1712.04248/) (2017)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Adversarial Training Methods for Semi-Supervised Text Classification](https://mlsanity.com/paper/1605.07725/) (2016)
- [Recent Advances in Adversarial Training for Adversarial Robustness](https://mlsanity.com/paper/2102.01356/) (2021)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examples](https://mlsanity.com/paper/1710.10766/) (2017)
- [Adversarial Logit Pairing](https://mlsanity.com/paper/1803.06373/) (2018)
- [Topology Attack and Defense for Graph Neural Networks: An Optimization Perspective](https://mlsanity.com/paper/1906.04214/) (2019)
- [Adversarial Training and Robustness for Multiple Perturbations](https://mlsanity.com/paper/1904.13000/) (2019)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [On the Convergence of Decentralized Gradient Descent](https://mlsanity.com/paper/1310.7063/) (2013)
- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)
- [Towards Deep Neural Network Architectures Robust to Adversarial Examples](https://mlsanity.com/paper/1412.5068/) (2014)
- [Adversarial Robustness through Local Linearization](https://mlsanity.com/paper/1907.02610/) (2019)
- [PixMix: Dreamlike Pictures Comprehensively Improve Safety Measures](https://mlsanity.com/paper/2112.05135/) (2021)
- [On the Convergence and Robustness of Adversarial Training](https://mlsanity.com/paper/2112.08304/) (2021)
- [Robustness and Accuracy Could Be Reconcilable by (Proper) Definition](https://mlsanity.com/paper/2202.10103/) (2022)
- [Graph Adversarial Training: Dynamically Regularizing Based on Graph Structure](https://mlsanity.com/paper/1902.08226/) (2019)

## Built on by (most cited first, 3 of 3)

- [Decentralized SGD and Average-direction SAM are Asymptotically Equivalent](https://mlsanity.com/paper/2306.02913/) (2023)
- [On the Escaping Efficiency of Distributed Adversarial Training Algorithms](https://mlsanity.com/paper/2509.11337/) (2025)
- [Stability and Generalization of Adversarial Diffusion Training](https://mlsanity.com/paper/2509.19234/) (2025)

## Abstract (arXiv)

The vulnerability of machine learning models to adversarial attacks has been attracting considerable attention in recent years. Most existing studies focus on the behavior of stand-alone single-agent learners. In comparison, this work studies adversarial training over graphs, where individual agents are subjected to perturbations of varied strength levels across space. It is expected that interactions by linked agents, and the heterogeneity of the attack models that are possible over the graph, can help enhance robustness in view of the coordination power of the group. Using a min-max formulation of distributed learning, we develop a decentralized adversarial training framework for multi-agent systems. Specifically, we devise two decentralized adversarial training algorithms by relying on two popular decentralized learning strategies--diffusion and consensus. We analyze the convergence properties of the proposed framework for strongly-convex, convex, and non-convex environments, and illustrate the enhanced robustness to adversarial attacks.