Adversarial attacks expose important vulnerabilities of deep learning models, yet little attention has been paid to settings where data arrives as a stream. In this paper, we formalize the online adversarial attack problem, emphasizing two key elements found in real-world use-cases: attackers must operate under partial knowledge of the target model, and the decisions made by the attacker are irrevocable since they operate on a transient data stream. We first rigorously analyze a deterministic variant of the online threat model by drawing parallels to the well-studied $k$-secretary problem in theoretical computer science and propose Virtual+, a simple yet practical online algorithm. Our main theoretical result show Virtual+ yields provably the best competitive ratio over all single-threshold algorithms for $k<5$ -- extending previous analysis of the $k$-secretary problem. We also introduce the textit{stochastic $k$-secretary} -- effectively reducing online blackbox transfer attacks to a $k$-secretary problem under noise -- and prove theoretical bounds on the performance of textit{any} online algorithms adapted to this setting. Finally, we complement our theoretical results by conducting experiments on both MNIST and CIFAR-10 with both vanilla and robust classifiers, revealing not only the necessity of online algorithms in achieving near-optimal performance but also the rich interplay of a given attack strategy towards online attack selection, enabling simple strategies like FGSM to outperform classically strong whitebox adversaries.
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