On the Convergence and Robustness of Adversarial Training (2112.08304v2)

Abstract: Improving the robustness of deep neural networks (DNNs) to adversarial examples is an important yet challenging problem for secure deep learning. Across existing defense techniques, adversarial training with Projected Gradient Decent (PGD) is amongst the most effective. Adversarial training solves a min-max optimization problem, with the \textit{inner maximization} generating adversarial examples by maximizing the classification loss, and the \textit{outer minimization} finding model parameters by minimizing the loss on adversarial examples generated from the inner maximization. A criterion that measures how well the inner maximization is solved is therefore crucial for adversarial training. In this paper, we propose such a criterion, namely First-Order Stationary Condition for constrained optimization (FOSC), to quantitatively evaluate the convergence quality of adversarial examples found in the inner maximization. With FOSC, we find that to ensure better robustness, it is essential to use adversarial examples with better convergence quality at the \textit{later stages} of training. Yet at the early stages, high convergence quality adversarial examples are not necessary and may even lead to poor robustness. Based on these observations, we propose a \textit{dynamic} training strategy to gradually increase the convergence quality of the generated adversarial examples, which significantly improves the robustness of adversarial training. Our theoretical and empirical results show the effectiveness of the proposed method.

• The paper presents the FOSC criterion as a novel measure to evaluate convergence quality in adversarial training.
• It proposes a dynamic training strategy that starts with weak adversarial examples and gradually employs stronger ones to improve robustness.
• The authors validate their approach through theoretical analysis and empirical experiments on benchmark datasets like MNIST and CIFAR-10.

On the Convergence and Robustness of Adversarial Training

In the paper titled "On the Convergence and Robustness of Adversarial Training," the authors present an investigation into the robustness of adversarial training, with a specific focus on deep neural networks (DNNs). The paper centers on improving DNN resilience against adversarial examples by examining the convergence characteristics of adversarial training methods, particularly those that employ Projected Gradient Descent (PGD).

Key Contributions

1. FOSC Criterion: The authors introduce the First-Order Stationary Condition for constrained optimization (FOSC) as a criterion to evaluate the convergence quality of adversarial examples generated during training. This criterion is crucial for quantifying the effectiveness of the inner maximization problem in the min-max optimization framework of adversarial training.
2. Dynamic Training Strategy: Based on findings from applying the FOSC criterion, the paper proposes a dynamic adversarial training strategy. This strategy advocates for the use of weak adversarial examples in the early training stages, followed by stronger ones as training progresses. This approach aims to optimize the convergence quality progressively, thereby enhancing robustness.
3. Theoretical and Empirical Validation: The researchers provide both theoretical convergence analysis and empirical experiments to demonstrate the efficacy of their proposed strategy. These findings suggest that the dynamic training method can yield superior robustness compared to standard adversarial training practices.

Technical Analysis

The research explores the interplay between the inner maximization and outer minimization steps in the adversarial training framework. The authors' notable contribution is the introduction of FOSC, a criterion that effectively correlates with adversarial strength and is more reliable than traditional loss-based metrics. The FOSC criterion measures how closely an adversarial example meets a first-order stationary point within the constrained optimization landscape, effectively assessing the adversarial example's convergence quality.

In exploring the convergence characteristics during different stages of adversarial training, the authors suggest that while high convergence quality adversarial examples are pivotal in later stages, they may not be beneficial early on. This insight forms the foundation of their dynamic training strategy, which incrementally increases the strength of adversarial examples throughout the training process. Experimentation on benchmark datasets such as MNIST and CIFAR-10, including architectures such as WideResNet, supports the robustness improvements claimed.

Implications and Future Directions

The findings suggest significant implications for the enhancement of DNN security in adversarial settings. By optimizing the training process through better-convergence-quality examples, the paper provides a pathway toward more resilient models against adversarial attacks.

Future developments could extend into further refinement of dynamic strategies, possibly incorporating more sophisticated criteria for adversarial strength and exploring the balance between clean input accuracy and adversarial robustness. Additionally, the broader landscape of adversarial defenses may benefit from incorporating these findings into new methodologies, possibly driving the development of hybrid approaches that leverage multiple facets of model defense.

The paper represents an important step in advancing the understanding and application of adversarial training, and it lays the groundwork for further refinement and exploration within the field of AI model security and robustness.