Data Poisoning Attack to X-armed Bandits

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.