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We study indiscriminate poisoning for linear learners where an adversary injects a few crafted examples into the training data with the goal of forcing the induced model to incur higher test error. Inspired by the observation that linear learners on some datasets are able to resist the best known attacks even without any defenses, we further investigate whether datasets can be inherently robust to indiscriminate poisoning attacks for linear learners. For theoretical Gaussian distributions, we rigorously characterize the behavior of an optimal poisoning attack, defined as the poisoning strategy that attains the maximum risk of the induced model at a given poisoning budget. Our results prove that linear learners can indeed be robust to indiscriminate poisoning if the class-wise data distributions are well-separated with low variance and the size of the constraint set containing all permissible poisoning points is also small. These findings largely explain the drastic variation in empirical attack performance of the state-of-the-art poisoning attacks on linear learners across benchmark datasets, making an important initial step towards understanding the underlying reasons some learning tasks are vulnerable to data poisoning attacks.more » « lessFree, publicly-accessible full text available December 11, 2024
null (Ed.)In a poisoning attack, an adversary with control over a small fraction of the training data attempts to select that data in a way that induces a corrupted model that misbehaves in favor of the adversary. We consider poisoning attacks against convex machine learning models and propose an efficient poisoning attack designed to induce a specified model. Unlike previous model-targeted poisoning attacks, our attack comes with provable convergence to any attainable target classifier. The distance from the induced classifier to the target classifier is inversely proportional to the square root of the number of poisoning points. We also provide a lower bound on the minimum number of poisoning points needed to achieve a given target classifier. Our method uses online convex optimization, so finds poisoning points incrementally. This provides more flexibility than previous attacks which require a priori assumption about the number of poisoning points. Our attack is the first model-targeted poisoning attack that provides provable convergence for convex models, and in our experiments, it either exceeds or matches state-of-the-art attacks in terms of attack success rate and distance to the target model.more » « less