Learning under $p$-Tampering Attacks
This work addresses security vulnerabilities in machine learning algorithms for scenarios where adversaries can tamper with training data, with incremental improvements over prior attacks.
The paper tackles the problem of learning under p-tampering attacks, presenting improved biasing attacks that increase error in targeted poisoning models and showing that PAC learning is possible in non-targeted settings under certain conditions, but not under more general adversarial noise.
Recently, Mahloujifar and Mahmoody (TCC'17) studied attacks against learning algorithms using a special case of Valiant's malicious noise, called $p$-tampering, in which the adversary gets to change any training example with independent probability $p$ but is limited to only choose malicious examples with correct labels. They obtained $p$-tampering attacks that increase the error probability in the so called targeted poisoning model in which the adversary's goal is to increase the loss of the trained hypothesis over a particular test example. At the heart of their attack was an efficient algorithm to bias the expected value of any bounded real-output function through $p$-tampering. In this work, we present new biasing attacks for increasing the expected value of bounded real-valued functions. Our improved biasing attacks, directly imply improved $p$-tampering attacks against learners in the targeted poisoning model. As a bonus, our attacks come with considerably simpler analysis. We also study the possibility of PAC learning under $p$-tampering attacks in the non-targeted (aka indiscriminate) setting where the adversary's goal is to increase the risk of the generated hypothesis (for a random test example). We show that PAC learning is possible under $p$-tampering poisoning attacks essentially whenever it is possible in the realizable setting without the attacks. We further show that PAC learning under "correct-label" adversarial noise is not possible in general, if the adversary could choose the (still limited to only $p$ fraction of) tampered examples that she substitutes with adversarially chosen ones. Our formal model for such "bounded-budget" tampering attackers is inspired by the notions of (strong) adaptive corruption in secure multi-party computation.