Recently, researchers have discovered that the state-of-the-art object classifiers can be fooled easily by small perturbations in the input unnoticeable to human eyes. It is known that an attacker can generate strong adversarial examples if she knows the classifier parameters. Conversely, a defender can robustify the classifier by retraining if she has the adversarial examples. The cat-and-mouse game nature of attacks and defenses raises the question of the presence of equilibria in the dynamics. In this paper, we present a neural-network based attack class to approximate a larger but intractable class of attacks, and formulate the attacker-defender interaction as a zero-sum leader-follower game. We present sensitivity-penalized optimization algorithms to find minimax solutions, which are the best worst-case defenses against whitebox attacks. Advantages of the learning-based attacks and defenses compared to gradient-based attacks and defenses are demonstrated with MNIST and CIFAR-10.
The authors describe a mechanism for defending against adversarial learning attacks on classifiers. They first consider the dynamics generated by the following procedure. They begin by training a classifier, generating attack samples using FGSM, then hardening the classifier by retraining with adversarial samples, generating new attack samples for the retrained classifier, and repeating.  
They next observe that since FGSM is given by a simple perturbation of the sample point by the gradient of the loss, that the fixed point of the above dynamics can be optimized for directly using gradient descent. They call this approach Sens FGSM, and evaluate it empirically against the various iterates of the above approach. 
They then generalize this approach to an arbitrary attacker strategy given by some parameter vector (e.g. a neural net for generating adversarial samples). In this case, the attacker and defender are playing a minimax game, and the authors propose finding the minimax (or maximin) parameters using an algorithm which alternates between maximization and minimization gradient steps. They conclude with empirical observations about the performance of this algorithm.
The paper is well-written and easy to follow. However, I found the empirical results to be a little underwhelming. Sens-FGSM outperforms the adversarial training defenses tuned for the “wrong” iteration, but it does not appear to perform particularly well with error rates well above 20%. How does it stack up against other defense approaches (e.g. https://arxiv.org/pdf/1705.09064.pdf)? Furthermore, what is the significance of FGSM-curr (FGSM-81) for Sens-FGSM? It is my understanding that Sens-FGSM is not trained to a particular iteration of the “cat-and-mouse” game. Why, then, does Sens-FGSM provide a consistently better defense against FGSM-81? With regards to the second part of the paper, using gradient methods to solve a minimax problem is not especially novel (i.e. Goodfellow et al.), thus I would liked to see more thorough experiments here as well. For example, it’s unlikely that the defender would ever know the attack network utilized by an attacker. How robust is the defense against samples generated by a different attack network? The authors seem to address this in section 5 by stating that the minimax solution is not meaningful for other network classes. However, this is a bit unsatisfying. Any defense can be *evaluated* against samples generated by any attacker strategy. Is it the case that the defenses fall flat against samples generated by different architectures? 
Minor Comments:
Section 3.1, First Line. ”f(ul(g(x),y))” appears to be a mistake.