# Improved Adversarial Training via Learned Optimizer

arXiv: https://arxiv.org/abs/2004.12227 · HTML: https://mlsanity.com/paper/2004.12227/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2020.

## Built on by (most cited first, 22 of 22)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [VeLO: Training Versatile Learned Optimizers by Scaling Up](https://mlsanity.com/paper/2211.09760/) (2022)
- [Practical tradeoffs between memory, compute, and performance in learned optimizers](https://mlsanity.com/paper/2203.11860/) (2022)
- [Generalizable Black-Box Adversarial Attack with Meta Learning](https://mlsanity.com/paper/2301.00364/) (2023)
- [Meta Adversarial Training against Universal Patches](https://mlsanity.com/paper/2101.11453/) (2021)
- [Neur2SP: Neural Two-Stage Stochastic Programming](https://mlsanity.com/paper/2205.12006/) (2022)
- [PointCAT: Contrastive Adversarial Training for Robust Point Cloud Recognition](https://mlsanity.com/paper/2209.07788/) (2022)
- [Learning to Generalize Provably in Learning to Optimize](https://mlsanity.com/paper/2302.11085/) (2023)
- [Meta-Learning the Search Distribution of Black-Box Random Search Based Adversarial Attacks](https://mlsanity.com/paper/2111.01714/) (2021)
- [Adversarial Framework with Certified Robustness for Time-Series Domain via Statistical Features](https://mlsanity.com/paper/2207.04307/) (2022)
- [Stochastic Unrolled Federated Learning](https://mlsanity.com/paper/2305.15371/) (2023)
- [Adversarial Training: A Survey](https://mlsanity.com/paper/2410.15042/) (2024)
- [Learning for Robust Combinatorial Optimization: Algorithm and Application](https://mlsanity.com/paper/2112.10377/) (2021)
- [M-L2O: Towards Generalizable Learning-to-Optimize by Test-Time Fast Self-Adaptation](https://mlsanity.com/paper/2303.00039/) (2023)
- [Model-Agnostic Meta-Attack: Towards Reliable Evaluation of Adversarial Robustness](https://mlsanity.com/paper/2110.08256/) (2021)
- [Is Scaling Learned Optimizers Worth It? Evaluating The Value of VeLO's 4000 TPU Months](https://mlsanity.com/paper/2310.18191/) (2023)
- [Optimizer Amalgamation](https://mlsanity.com/paper/2203.06474/) (2022)
- [Training Robust Deep Models for Time-Series Domain: Novel Algorithms and Theoretical Analysis](https://mlsanity.com/paper/2207.04305/) (2022)
- [Adversarial Threats in Quantum Machine Learning: A Survey of Attacks and Defenses](https://mlsanity.com/paper/2506.21842/) (2025)
- [HUB: Guiding Learned Optimizers with Continuous Prompt Tuning](https://mlsanity.com/paper/2305.16823/) (2023)
- [MACS: Multi-Agent Reinforcement Learning for Optimization of Crystal Structures](https://mlsanity.com/paper/2506.04195/) (2025)
- [Unveiling the Backdoor Mechanism Hidden Behind Catastrophic Overfitting in Fast Adversarial Training](https://mlsanity.com/paper/2604.24350/) (2026)

## Abstract (arXiv)

Adversarial attack has recently become a tremendous threat to deep learning models. To improve the robustness of machine learning models, adversarial training, formulated as a minimax optimization problem, has been recognized as one of the most effective defense mechanisms. However, the non-convex and non-concave property poses a great challenge to the minimax training. In this paper, we empirically demonstrate that the commonly used PGD attack may not be optimal for inner maximization, and improved inner optimizer can lead to a more robust model. Then we leverage a learning-to-learn (L2L) framework to train an optimizer with recurrent neural networks, providing update directions and steps adaptively for the inner problem. By co-training optimizer's parameters and model's weights, the proposed framework consistently improves the model robustness over PGD-based adversarial training and TRADES.