A quantum active learning algorithm for sampling against adversarial attacks

Adversarial attacks represent a serious menace for learning algorithms and may compromise the security of future autonomous systems. A theorem by Khoury and Hadfield-Menell (KH), provides sufficient conditions to guarantee the robustness of active learning algorithms, but comes with a caveat: it is crucial to know the smallest distance among the classes of the corresponding classification problem. We propose a theoretical framework that allows us to think of active learning as sampling the most promising new points to be classified, so that the minimum distance between classes can be found and the theorem KH used. The complexity of the quantum active learning algorithm is polynomial in the variables used, like the dimension of the space $m$ and the size of the initial training data $n$. On the other hand, if one replicates this approach with a classical computer, we expect that it would take exponential time in $m$, an example of the so-called `curse of dimensionality'.