# Adversarial Attack Generation Empowered by Min-Max Optimization

arXiv: https://arxiv.org/abs/1906.03563 · HTML: https://mlsanity.com/paper/1906.03563/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2019.

## Built on by (most cited first, 30 of 32)

- [Boosting the Transferability of Adversarial Attacks with Reverse Adversarial Perturbation](https://mlsanity.com/paper/2210.05968/) (2022)
- [Federated Minimax Optimization: Improved Convergence Analyses and Algorithms](https://mlsanity.com/paper/2203.04850/) (2022)
- [Optimal Algorithms for Stochastic Bilevel Optimization under Relaxed Smoothness Conditions](https://mlsanity.com/paper/2306.12067/) (2023)
- [Towards Compositional Adversarial Robustness: Generalizing Adversarial Training to Composite Semantic Perturbations](https://mlsanity.com/paper/2202.04235/) (2022)
- [Single-Call Stochastic Extragradient Methods for Structured Non-monotone Variational Inequalities: Improved Analysis under Weaker Conditions](https://mlsanity.com/paper/2302.14043/) (2023)
- [Take the Bull by the Horns: Hard Sample-Reweighted Continual Training Improves LLM Generalization](https://mlsanity.com/paper/2402.14270/) (2024)
- [Holistic Adversarial Robustness of Deep Learning Models](https://mlsanity.com/paper/2202.07201/) (2022)
- [Solving a Class of Non-Convex Minimax Optimization in Federated Learning](https://mlsanity.com/paper/2310.03613/) (2023)
- [Adv3D: Generating Safety-Critical 3D Objects through Closed-Loop Simulation](https://mlsanity.com/paper/2311.01446/) (2023)
- [A first-order augmented Lagrangian method for constrained minimax optimization](https://mlsanity.com/paper/2301.02060/) (2023)
- [Submodular Minimax Optimization: Finding Effective Sets](https://mlsanity.com/paper/2305.16903/) (2023)
- [Communication-Efficient Gradient Descent-Accent Methods for Distributed Variational Inequalities: Unified Analysis and Local Updates](https://mlsanity.com/paper/2306.05100/) (2023)
- [On Adversarial Robustness of Point Cloud Semantic Segmentation](https://mlsanity.com/paper/2112.05871/) (2021)
- [Generating Adversarial Examples with Task Oriented Multi-Objective Optimization](https://mlsanity.com/paper/2304.13229/) (2023)
- [Doubly Robust Instance-Reweighted Adversarial Training](https://mlsanity.com/paper/2308.00311/) (2023)
- [Faster Stochastic Variance Reduction Methods for Compositional MiniMax Optimization](https://mlsanity.com/paper/2308.09604/) (2023)
- [FINEST: Stabilizing Recommendations by Rank-Preserving Fine-Tuning](https://mlsanity.com/paper/2402.03481/) (2024)
- [Towards Fair Class-wise Robustness: Class Optimal Distribution Adversarial Training](https://mlsanity.com/paper/2501.04527/) (2025)
- [Solving the Offline and Online Min-Max Problem of Non-smooth Submodular-Concave Functions: A Zeroth-Order Approach](https://mlsanity.com/paper/2601.21243/) (2026)
- [Achieving Near-Optimal Convergence for Distributed Minimax Optimization with Adaptive Stepsizes](https://mlsanity.com/paper/2406.02939/) (2024)
- [Robustness of Agentic AI Systems via Adversarially-Aligned Jacobian Regularization](https://mlsanity.com/paper/2603.04378/) (2026)
- [Shuffling the Data, Stretching the Step-size: Sharper Bias in constant step-size SGD](https://mlsanity.com/paper/2604.10373/) (2026)
- [On visual self-supervision and its effect on model robustness](https://mlsanity.com/paper/2112.04367/) (2021)
- [Bridging Models to Defend: A Population-Based Strategy for Robust Adversarial Defense](https://mlsanity.com/paper/2303.10225/) (2023)
- [Learning to Model Graph Structural Information on MLPs via Graph Structure Self-Contrasting](https://mlsanity.com/paper/2409.05573/) (2024)
- [Shuffling Gradient-Based Methods for Nonconvex-Concave Minimax Optimization](https://mlsanity.com/paper/2410.22297/) (2024)
- [Learning task-specific predictive models for scientific computing](https://mlsanity.com/paper/2506.03835/) (2025)
- [ROBAD: Robust Adversary-aware Local-Global Attended Bad Actor Detection Sequential Model](https://mlsanity.com/paper/2507.15067/) (2025)
- [A first-order method for nonconvex-strongly-concave constrained minimax optimization](https://mlsanity.com/paper/2512.22909/) (2025)
- [Adversarial Update-Based Federated Unlearning for Poisoned Model Recovery](https://mlsanity.com/paper/2605.02110/) (2026)

## Abstract (arXiv)

The worst-case training principle that minimizes the maximal adversarial loss, also known as adversarial training (AT), has shown to be a state-of-the-art approach for enhancing adversarial robustness. Nevertheless, min-max optimization beyond the purpose of AT has not been rigorously explored in the adversarial context. In this paper, we show how a general framework of min-max optimization over multiple domains can be leveraged to advance the design of different types of adversarial attacks. In particular, given a set of risk sources, minimizing the worst-case attack loss can be reformulated as a min-max problem by introducing domain weights that are maximized over the probability simplex of the domain set. We showcase this unified framework in three attack generation problems -- attacking model ensembles, devising universal perturbation under multiple inputs, and crafting attacks resilient to data transformations. Extensive experiments demonstrate that our approach leads to substantial attack improvement over the existing heuristic strategies as well as robustness improvement over state-of-the-art defense methods trained to be robust against multiple perturbation types. Furthermore, we find that the self-adjusted domain weights learned from our min-max framework can provide a holistic tool to explain the difficulty level of attack across domains. Code is available at https://github.com/wangjksjtu/minmax-adv.