How Robust are Randomized Smoothing based Defenses to Data Poisoning?

The prediction of certifiably robust classifiers remains constant around 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 robustness. Specifically, we propose a novel bilevel optimization based data poisoning attack that degrades the robustness guarantees of certifiably robust classifiers. Unlike other data poisoning attacks that reduce the accuracy of the poisoned models on a small set of target points, our attack reduces the average certified radius 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}. To make the attack harder to detect we use clean-label poisoning points with imperceptibly small distortions. The effectiveness of the proposed method is evaluated by poisoning MNIST and CIFAR10 datasets and training deep neural networks using the previously mentioned robust training methods and certifying their robustness using randomized smoothing. For the models trained with these robust training methods our attack points reduce the average certified radius of the target class by more than 30% and are transferable to models with different architectures and models trained with different robust training methods.