Black-Box Adversarial Attack on Time Series Classification

With the increasing use of deep neural networks (DNN) in time series classification (TSC), recent work reveals the threat of adversarial attack, where the adversary can construct adversarial examples to cause model mistakes. However, existing research on the adversarial attack of TSC typically adopts an unrealistic white-box setting with model details transparent to the adversary. In this work, we study a more rigorous black-box setting with attack detection applied, which restricts gradient access and requires the adversarial example to be also stealthy. Theoretical analyses reveal that the key lies in: estimating black-box gradient with diversity and non-convexity of TSC models resolved, and restricting the ℓ0 norm of the perturbation to construct adversarial samples. Towards this end, we propose a new framework named Black-TreeS, which solves the hard optimization issue for adversarial example construction with two simple yet effective modules. In particular, we propose a tree search strategy to find influential positions in a sequence, and independently estimate the black-box gradients for these positions. Extensive experiments on three real-world TSC datasets and five DNN based models validate the effectiveness of BlackTreeS, e.g., it improves the attack success rate from 19.3% to 27.3%, and decreases the detection success rate from 90.9% to 6.8% for LSTM on the UWave dataset.