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.
Lastly, a related framework of finding minimax risk was also studied in @cite_0 for the purpose of preventing attacks on privacy. We discuss how the attack on classification in this paper and the attack on privacy are the two sides of the same optimization problem with the opposite goals.
@cite_0
2765886485
Preserving the utility of published datasets while simultaneously providing provable privacy guarantees is a well-known challenge. On the one hand, context-free privacy solutions, such as differential privacy, provide strong privacy guarantees, but often lead to a significant reduction in utility. On the other hand, context-aware privacy solutions, such as information theoretic privacy, achieve an improved privacy-utility tradeoff, but assume that the data holder has access to dataset statistics. We circumvent these limitations by introducing a novel context-aware privacy framework called generative adversarial privacy (GAP). GAP leverages recent advancements in generative adversarial networks (GANs) to allow the data holder to learn privatization schemes from the dataset itself. Under GAP, learning the privacy mechanism is formulated as a constrained minimax game between two players: a privatizer that sanitizes the dataset in a way that limits the risk of inference attacks on the individuals’ private variables, and an adversary that tries to infer the private variables from the sanitized dataset. To evaluate GAP’s performance, we investigate two simple (yet canonical) statistical dataset models: (a) the binary data model; and (b) the binary Gaussian mixture model. For both models, we derive game-theoretically optimal minimax privacy mechanisms, and show that the privacy mechanisms learned from data (in a generative adversarial fashion) match the theoretically optimal ones. This demonstrates that our framework can be easily applied in practice, even in the absence of dataset statistics.