# Nash Equilibria and Pitfalls of Adversarial Training in Adversarial Robustness Games

arXiv: https://arxiv.org/abs/2210.12606 · HTML: https://mlsanity.com/paper/2210.12606/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 59 references that are in the map.
- First posted on arXiv 23 Oct 2022.

## Builds on (most cited first, 30 of 40)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [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)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Feature Denoising for Improving Adversarial Robustness](https://mlsanity.com/paper/1812.03411/) (2018)
- [Improving Robustness using Generated Data](https://mlsanity.com/paper/2110.09468/) (2021)
- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [Data Augmentation Can Improve Robustness](https://mlsanity.com/paper/2111.05328/) (2021)
- [A Universal Law of Robustness via Isoperimetry](https://mlsanity.com/paper/2105.12806/) (2021)
- [Fast Convergence of Regularized Learning in Games](https://mlsanity.com/paper/1507.00407/) (2015)
- [Understanding and Mitigating the Tradeoff Between Robustness and Accuracy](https://mlsanity.com/paper/2002.10716/) (2020)
- [Adversarial Robustness through Local Linearization](https://mlsanity.com/paper/1907.02610/) (2019)
- [Cycles in adversarial regularized learning](https://mlsanity.com/paper/1709.02738/) (2017)
- [Robust Learning Meets Generative Models: Can Proxy Distributions Improve Adversarial Robustness?](https://mlsanity.com/paper/2104.09425/) (2021)
- [Feature Purification: How Adversarial Training Performs Robust Deep Learning](https://mlsanity.com/paper/2005.10190/) (2020)
- [Precise Tradeoffs in Adversarial Training for Linear Regression](https://mlsanity.com/paper/2002.10477/) (2020)
- [Adversarially Robust Generalization Just Requires More Unlabeled Data](https://mlsanity.com/paper/1906.00555/) (2019)
- [A law of robustness for two-layers neural networks](https://mlsanity.com/paper/2009.14444/) (2020)
- [Randomization matters. How to defend against strong adversarial attacks](https://mlsanity.com/paper/2002.11565/) (2020)
- [Adversarial Example Games](https://mlsanity.com/paper/2007.00720/) (2020)

## Built on by (most cited first, 8 of 8)

- [Balance, Imbalance, and Rebalance: Understanding Robust Overfitting from a Minimax Game Perspective](https://mlsanity.com/paper/2310.19360/) (2023)
- [Reliable learning in challenging environments](https://mlsanity.com/paper/2304.03370/) (2023)
- [On the existence of solutions to adversarial training in multiclass classification](https://mlsanity.com/paper/2305.00075/) (2023)
- [Game Theoretic Mixed Experts for Combinational Adversarial Machine Learning](https://mlsanity.com/paper/2211.14669/) (2022)
- [Responsible AI (RAI) Games and Ensembles](https://mlsanity.com/paper/2310.18832/) (2023)
- [Paths to Equilibrium in Games](https://mlsanity.com/paper/2403.18079/) (2024)
- [Position: Towards Resilience Against Adversarial Examples](https://mlsanity.com/paper/2405.01349/) (2024)
- [Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transport](https://mlsanity.com/paper/2609.22240/) (2026)

## Abstract (arXiv)

Adversarial training is a standard technique for training adversarially robust models. In this paper, we study adversarial training as an alternating best-response strategy in a 2-player zero-sum game. We prove that even in a simple scenario of a linear classifier and a statistical model that abstracts robust vs. non-robust features, the alternating best response strategy of such game may not converge. On the other hand, a unique pure Nash equilibrium of the game exists and is provably robust. We support our theoretical results with experiments, showing the non-convergence of adversarial training and the robustness of Nash equilibrium.