Machine vs Machine: Minimax-Optimal Defense Against Adversarial Examples
This work addresses the vulnerability of state-of-the-art classifiers to adversarial attacks, which is a critical security issue in machine learning, but it is incremental as it builds on existing game-theoretic formulations and focuses on specific attack types.
The paper tackles the problem of defending against adversarial examples in object classifiers by formulating it as a two-player continuous zero-sum game and proposing a minimax optimization algorithm to find the best worst-case defense against whitebox attacks. Experiments on MNIST and CIFAR-10 datasets show that this defense is more robust than non-minimax defenses, though specific numerical gains are not provided.
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 also 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 access to the adversarial examples. We explain and formulate this adversarial example problem as a two-player continuous zero-sum game, and demonstrate the fallacy of evaluating a defense or an attack as a static problem. To find the best worst-case defense against whitebox attacks, we propose a continuous minimax optimization algorithm. We demonstrate the minimax defense with two types of attack classes -- gradient-based and neural network-based attacks. Experiments with the MNIST and the CIFAR-10 datasets demonstrate that the defense found by numerical minimax optimization is indeed more robust than non-minimax defenses. We discuss directions for improving the result toward achieving robustness against multiple types of attack classes.