# Unveiling and Mitigating Adversarial Vulnerabilities in Iterative Optimizers

arXiv: https://arxiv.org/abs/2504.19000 · HTML: https://mlsanity.com/paper/2504.19000/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 58 references that are in the map.
- First posted on arXiv 26 Apr 2025.

## Builds on (most cited first, 30 of 34)

- [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)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Nesterov Accelerated Gradient and Scale Invariance for Adversarial Attacks](https://mlsanity.com/paper/1908.06281/) (2019)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [Advances in adversarial attacks and defenses in computer vision: A survey](https://mlsanity.com/paper/2108.00401/) (2021)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Efficient Algorithms for Smooth Minimax Optimization](https://mlsanity.com/paper/1907.01543/) (2019)
- [Revisiting and Advancing Fast Adversarial Training Through The Lens of Bi-Level Optimization](https://mlsanity.com/paper/2112.12376/) (2021)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [Opportunities and Challenges in Deep Learning Adversarial Robustness: A Survey](https://mlsanity.com/paper/2007.00753/) (2020)
- [Understanding Adversarial Examples from the Mutual Influence of Images and Perturbations](https://mlsanity.com/paper/2007.06189/) (2020)
- [Solving Inverse Problems With Deep Neural Networks -- Robustness Included?](https://mlsanity.com/paper/2011.04268/) (2020)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Non-convex Robust PCA](https://mlsanity.com/paper/1410.7660/) (2014)
- [Unrolled Optimization with Deep Priors](https://mlsanity.com/paper/1705.08041/) (2017)
- [Learning Convex Optimization Control Policies](https://mlsanity.com/paper/1912.09529/) (2019)
- [Ada-LISTA: Learned Solvers Adaptive to Varying Models](https://mlsanity.com/paper/2001.08456/) (2020)
- [Hyperparameter Tuning is All You Need for LISTA](https://mlsanity.com/paper/2110.15900/) (2021)
- [A Practical Guide to Robust Optimization](https://mlsanity.com/paper/1501.02634/) (2015)
- [Learning Convex Optimization Models](https://mlsanity.com/paper/2006.04248/) (2020)
- [Adversarial Examples Are Not Real Features](https://mlsanity.com/paper/2310.18936/) (2023)

## Built on by (most cited first, 4 of 4)

- [Deep Unfolding: Recent Developments, Theory, and Design Guidelines](https://mlsanity.com/paper/2512.03768/) (2025)
- [Adversarial Threats in Quantum Machine Learning: A Survey of Attacks and Defenses](https://mlsanity.com/paper/2506.21842/) (2025)
- [On Inverse Problems, Parameter Estimation, and Domain Generalization](https://mlsanity.com/paper/2506.06024/) (2025)
- [MANET-GNN: Learned Decentralized Optimization of Power Allocation in Multi-Channel MANETs](https://mlsanity.com/paper/2609.40170/) (2026)

## Abstract (arXiv)

Machine learning (ML) models are often sensitive to carefully crafted yet seemingly unnoticeable perturbations. Such adversarial examples are considered to be a property of ML models, often associated with their black-box operation and sensitivity to features learned from data. This work examines the adversarial sensitivity of non-learned decision rules, and particularly of iterative optimizers. Our analysis is inspired by the recent developments in deep unfolding, which cast such optimizers as ML models. We show that non-learned iterative optimizers share the sensitivity to adversarial examples of ML models, and that attacking iterative optimizers effectively alters the optimization objective surface in a manner that modifies the minima sought. We then leverage the ability to cast iteration-limited optimizers as ML models to enhance robustness via adversarial training. For a class of proximal gradient optimizers, we rigorously prove how their learning affects adversarial sensitivity. We numerically back our findings, showing the vulnerability of various optimizers, as well as the robustness induced by unfolding and adversarial training.