X-armed bandits have achieved the state-of-the-art performance in optimizing unknown stochastic continuous functions, which can model many machine learning tasks, specially in big data-driven personalized recommendation. However, bandit algorithms are vulnerable to adversarial attacks. Existing works mainly focus on attacking multi-armed bandits in discrete setting; nevertheless, the attacks against X-armed bandits in continuous setting have not been well explored. In this paper, we aim to bridge this gap and investigate the robustness problem for the X-armed bandits. Specifically, we consider data poisoning attack and propose an attack algorithm named Confidence Poisoning Attack algorithm, which could hijack the clean tree-based X-armed bandits algorithm, i.e., high confidence tree (HCT) and make it choose the nodes including the arm targeted by the attacker very frequently with a sub-linear attack cost, i.e., O(Tα)(0 <α< 1), where T is the total number of rounds. We evaluate the efficiency of our proposed attack algorithm through theoretical analysis and experiments.

As a continuous variant of Multi-armed bandits (MAB), $\mathcal{X}$-armed bandits have enriched many applications of online machine learning like personalized recommendation system. However, the attack and defense to the $\mathcal{X}$-armed bandits remain largely unexplored, though the MAB has proved to be vulnerable. In this paper, we aim to bridge this gap and investigate the robustness analysis for the $\mathcal{X}$-armed bandits. Specifically, we consider action-manipulation attack, which is practical but harder than the existing reward-manipulation attack. We propose an attack algorithm based on a lower bound tree (LBT), which can continuously hijack the learner’s action by perturbing $\mathcal{X}$-armed bandits’ high confidence tree (HCT) construction. As a result, the nodes including the arm targeted by the attacker is selected frequently with a sublinear attack cost. To defend against the LBT attack, we propose a robust version of the HCT algorithm, called RoHCT. We theoretically analyze that the regret of RoHCT is related to the upper bound of the total cost Q and still sublinear to total number of rounds T. We carry out experiments to evaluate the effectiveness of LBT and RoHCT.

High resolution and accurate location are the crucial goals associated with the application of guided waves for nondestructive testing purposes. In this paper, through experimental studies, the influences of the frequency-dependent amplitude to the testing resolution of guided wave methods are investigated. Firstly, the factors which result in frequency dependency to the amplitude characteristic of guided wave modes are investigated. Then, the influences of the frequency-dependent amplitude to the spectrum of guided wave mode propagating in the structure are analyzed. The results show that it brings amplitude modulation to guided wave modes, resulting in peak frequency shifting and bandwidth variation in their spectra. This spectrum distortion affects the wave form of the received wave packet (i.e., time duration), and further the testing resolution of guided wave modes. Ultimately, two simple and universal experimental cases are introduced to verify and illustrate these effects. The results show that because of the frequency-dependent amplitude, the testing resolution of guided wave modes is still limited even when either time reversal technique or dispersion compensation is applied.