Conformal Prediction (CP) is a popular uncertainty quantification method that
provides distribution-free, statistically valid prediction sets, assuming that
training and test data are exchangeable. In such a case, CP's prediction sets
are guaranteed to cover the (unknown) true test output with a user-specified
probability. Nevertheless, this guarantee is violated when the data is
subjected to adversarial attacks, which often result in a significant loss of
coverage. Recently, several approaches have been put forward to recover CP
guarantees in this setting. These approaches leverage variations of randomised
smoothing to produce conservative sets which account for the effect of the
adversarial perturbations. They are, however, limited in that they only support
$\ell^2$-bounded perturbations and classification tasks. This paper introduces
\emph{VRCP (Verifiably Robust Conformal Prediction)}, a new framework that
leverages recent neural network verification methods to recover coverage
guarantees under adversarial attacks. Our VRCP method is the first to support
perturbations bounded by arbitrary norms including $\ell^1$, $\ell^2$, and
$\ell^\infty$, as well as regression tasks. We evaluate and compare our
approach on image classification tasks (CIFAR10, CIFAR100, and TinyImageNet)
and regression tasks for deep reinforcement learning environments. In every
case, VRCP achieves above nominal coverage and yields significantly more
efficient and informative prediction regions than the SotA.

使用最新的神经网络验证方法，基于 VRCP（可验证鲁棒性适应预测）框架，本文提出了一种新的方法，用于恢复在遭受对抗攻击时的预测覆盖率保证，并支持任意范数的扰动和回归任务，实验结果表明，在图像分类和强化学习环境的回归任务中，VRCP 方法达到了超过标称覆盖率的结果，并且比目前最先进的方法更高效且信息量更丰富。