Gaussian processes (GP) are a widely-adopted tool used to sequentially optimize black-box functions, where evaluations are costly and potentially noisy. Recent works on GP bandits have proposed to move beyond random noise and devise algorithms robust to adversarial attacks. In this paper, we study this problem from the attacker's perspective, proposing various adversarial attack methods with differing assumptions on the attacker's strength and prior information. Our goal is to understand adversarial attacks on GP bandits from both a theoretical and practical perspective. We focus primarily on targeted attacks on the popular GP-UCB algorithm and a related elimination-based algorithm, based on adversarially perturbing the function $f$ to produce another function $\tilde{f}$ whose optima are in some region $\mathcal{R}_{\rm target}$. Based on our theoretical analysis, we devise both white-box attacks (known $f$) and black-box attacks (unknown $f$), with the former including a Subtraction attack and Clipping attack, and the latter including an Aggressive subtraction attack. We demonstrate that adversarial attacks on GP bandits can succeed in forcing the algorithm towards $\mathcal{R}_{\rm target}$ even with a low attack budget, and we compare our attacks' performance and efficiency on several real and synthetic functions.

Motivated by the need of solving machine learning problems over distributed datasets, we explore the use of coreset to reduce the communication overhead. Coreset is a summary of the original dataset in the form of a small weighted set in the same sample space. Compared to other data summaries, coreset has the advantage that it can be used as a proxy of the original dataset, potentially for different applications. However, existing coreset construction algorithms are each tailor-made for a specific machine learning problem. Thus, to solve different machine learning problems, one has to collect coresets of different types, defeating the purpose of saving communication overhead. We resolve this dilemma by developing coreset construction algorithms based on k-means/median clustering, that give a provably good approximation for a broad range of machine learning problems with sufficiently continuous cost functions. Through evaluations on diverse datasets and machine learning problems, we verify the robust performance of the proposed algorithms.