  Neural networks are vulnerable to adversarial attacks: adding well-crafted,
imperceptible perturbations to their input can modify their output. Adversarial
training is one of the most effective approaches to training robust models
against such attacks. Unfortunately, this method is much slower than vanilla
training of neural networks since it needs to construct adversarial examples
for the entire training data at every iteration. By leveraging the theory of
coreset selection, we show how selecting a small subset of training data
provides a principled approach to reducing the time complexity of robust
training. To this end, we first provide convergence guarantees for adversarial
coreset selection. In particular, we show that the convergence bound is
directly related to how well our coresets can approximate the gradient computed
over the entire training data. Motivated by our theoretical analysis, we
propose using this gradient approximation error as our adversarial coreset
selection objective to reduce the training set size effectively. Once built, we
run adversarial training over this subset of the training data. Unlike existing
methods, our approach can be adapted to a wide variety of training objectives,
including TRADES, $\ell_p$-PGD, and Perceptual Adversarial Training. We conduct
extensive experiments to demonstrate that our approach speeds up adversarial
training by 2-3 times while experiencing a slight degradation in the clean and
robust accuracy.
