  Predictions of certifiably robust classifiers remain constant in a
neighborhood of a point, making them resilient to test-time attacks with a
guarantee. In this work, we present a previously unrecognized threat to robust
machine learning models that highlights the importance of training-data quality
in achieving high certified adversarial robustness. Specifically, we propose a
novel bilevel optimization-based data poisoning attack that degrades the
robustness guarantees of certifiably robust classifiers. Unlike other poisoning
attacks that reduce the accuracy of the poisoned models on a small set of
target points, our attack reduces the average certified radius (ACR) of an
entire target class in the dataset. Moreover, our attack is effective even when
the victim trains the models from scratch using state-of-the-art robust
training methods such as Gaussian data augmentation\cite{cohen2019certified},
MACER\cite{zhai2020macer}, and SmoothAdv\cite{salman2019provably} that achieve
high certified adversarial robustness. To make the attack harder to detect, we
use clean-label poisoning points with imperceptible distortions. The
effectiveness of the proposed method is evaluated by poisoning MNIST and
CIFAR10 datasets and training deep neural networks using previously mentioned
training methods and certifying the robustness with randomized smoothing. The
ACR of the target class, for models trained on generated poison data, can be
reduced by more than 30\%. Moreover, the poisoned data is transferable to
models trained with different training methods and models with different
architectures.
