Poisoning Attack Against Estimating From Pairwise Comparisons

As pairwise ranking becomes broadly employed for elections, sports competitions, recommendation, information retrieval and so on, attackers have strong motivation and incentives to manipulate or disrupt the ranking list. They could inject malicious comparisons into the training data to fool the target ranking algorithm. Such a technique is called "poisoning attack" in regression and classification tasks. In this paper, to the best of our knowledge, we initiate the first systematic investigation of data poisoning attack on the pairwise ranking algorithms, which can be generally formalized as the dynamic and static games between the ranker and the attacker, and can be modeled as certain kinds of integer programming problems mathematically. To break the computational hurdle of the underlying integer programming problems, we reformulate them into the distributionally robust optimization (DRO) problems, which are computational tractable. Based on such DRO formulations, we propose two efficient poisoning attack algorithms and establish the associated theoretical guarantees including the existence of Nash equilibrium and the generalization ability bounds. The effectiveness of the suggested poisoning attack strategies is demonstrated by a series of toy simulations and several real data experiments. These experimental results show that the proposed methods can significantly reduce the performance of the ranker in the sense that the correlation between the true ranking list and the aggregated results with toxic data can be decreased dramatically.