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 against norm-ball bounded input perturbations. Nonetheless, min-max optimization beyond the purpose of AT has not been rigorously explored in the research of adversarial attack and defense. In particular, given a set of risk sources (domains), minimizing the maximal loss induced from the domain set can be reformulated as a general min-max problem that is fundamentally different from AT since the maximization is taken over the probability simplex of the domain set. Examples of this general formulation include attacking model ensembles, devising universal perturbation under multiple inputs or data transformations, and generalized AT over different types of attack models. We show that these problems can be solved under a unified and theoretically principled min-max optimization framework. We also show that the self-adjusted domain weights learnt from our method provide a holistic tool to explain the difficulty level of attack and defense over multiple domains. Extensive experiments show that our approach leads to substantial performance improvement over the conventional heuristic strategies 1 .
Note: I applied a higher standard to this paper given that it significantly exceeds the recommended page limit. Furthermore, important details are left out in the appendices, which make it difficult to read the main body of the paper in a self-contained fashion. Given that the main body was already over the recommended page limit, I did not read the appendices.
This paper generalizes the min max formulation of adversarial training, and proposes a formulation that encompasses adversarial training of an ensemble, robustness to universal adversarial examples, and robustness to non-adversarial transformations. This formulation is used to derive an adversarial training procedure that trains against the worst-case adversarial example among adversarial examples generated by a set of attacks. Experiments seek to demonstrate applicability of this framework to both attacks and defenses.
As far as experiments are concerned, Section 4.1 presents results on MNIST, which is known to be a poor dataset to study adversarial examples on [https://arxiv.org/abs/1902.06705]. If models C and D are more difficult to attack, could better baselines be employed than attacking the ensemble A+B+C+D? For instance, would an adversary evading models C+D only perform better? It is difficult to draw insights that are generally applicable from a single ensemble. How was the ensemble chosen? Why would a defender add models which are known to be significantly less robust to the ensemble?
When discussing universal perturbations, how are they generated? Given that the performance of the proposed approach significantly degrades average evasion across all images from all groups, what is the threat model for an adversary being interested in group-level success rather than average evasion across all images from all groups? How were the values of K chosen? This comment also 	applies to experiments over data transformations. For these experiments, what was the value of K?
As far as the defensive perspective is concerned, it is not clear whether the improvements observed are statistically significant. Were multiple runs averaged to produce Table 4? Given that without DPAR, the improvement is negligible, this is important to interpret results. It appears that most of the robustness gains in both the average and max settings stem from DPAR. This should be clearly surfaced in the introduction and presentation of contributions if DPAR is required for the proposed generalized min max formulation to improve robustness. In particular, it is not clear whether DPAR is “a beneficial supplement to adversarial training” or a required supplement to adversarial training - per the formulation in this paper.
There are issues with grammar throughout the document, which make it difficult to read. Some specific issues:
1 - Adversarial attack is a tautology (an attack is always adversarial)
7 - What does “robust” adversarial attack mean?
7 - What is CAAD-18?
7 - Define ASR_all: what does evade mean here? Is the attack targeted or untargeted?
7 - What is an “advanced” DNN?