Learning under p-tampering poisoning attacks

Recently, Mahloujifar and Mahmoody (Theory of Cryptography Conference’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 ‘adversarial’ 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 ‘no-mistake’ adversarial noise is not possible, 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 adaptive corruption in cryptography.