Query-Efficient and Imperceptible Attacks on Multivariate Time Series DNN Models

Many black-box adversarial attacks for deep neural network (DNN) models for two-dimensional image datasets have been proposed. Though there are many pervasive and computing application scenarios that need multivariate time-series data as DNN inputs, little research has been devoted to black-box adversarial attacks on multivariate time-series DNN models, which have higher requirements on efficiency and imperceptibility. To meet the requirements, in this paper, we propose three different black-box adversarial attacks based on an existing attack: a self-adaptive step technique to improve the query-efficiency and success rate; an $L_{0}$ distance-based attack to improve imperceptibility; and an input coordinate importance oriented attack based on multiplicative weight update (MWU), which exploits the time-series structure and improves query-efficiency and imperceptibility. These proposed attacks are able to make trade-offs between successful rate, $L_{2}/L_{0}$ distance, and the number of queries tailored for a particular targeted attack task. We conducted extensive experiments using ten different combinations of DNN models and datasets to test the effectiveness of the proposed black-box adversarial attacks for multivariate time-series based DNNs. The proposed attacks achieve up to 51% higher success rates with 25% fewer queries, and 84% fewer perturbation amounts over the existing black-box adversarial attacks.