Multi-party Poisoning through Generalized p-Tampering
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In a poisoning attack against a learning algorithm, an adversary tampers with a fraction of the training data T with the goal of increasing the classification error of the constructed hypothesis/model over the final test distribution. In the distributed setting, T might be gathered gradually from m data providers P_1,...,P_m who generate and submit their shares of T in an online way. In this work, we initiate a formal study of (k,p)-poisoning attacks in which an adversary controls k∈[n] of the parties, and even for each corrupted party P_i, the adversary submits some poisoned data T'_i on behalf of P_i that is still "(1-p)-close" to the correct data T_i (e.g., 1-p fraction of T'_i is still honestly generated). For k=m, this model becomes the traditional notion of poisoning, and for p=1 it coincides with the standard notion of corruption in multi-party computation. We prove that if there is an initial constant error for the generated hypothesis h, there is always a (k,p)-poisoning attacker who can decrease the confidence of h (to have a small error), or alternatively increase the error of h, by Ω(p · k/m). Our attacks can be implemented in polynomial time given samples from the correct data, and they use no wrong labels if the original distributions are not noisy. At a technical level, we prove a general lemma about biasing bounded functions f(x_1,...,x_n)∈[0,1] through an attack model in which each block x_i might be controlled by an adversary with marginal probability p in an online way. When the probabilities are independent, this coincides with the model of p-tampering attacks, thus we call our model generalized p-tampering. We prove the power of such attacks by incorporating ideas from the context of coin-flipping attacks into the p-tampering model and generalize the results in both of these areas.
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