QCRS: Improve Randomized Smoothing using Quasi-Concave Optimization

Randomized smoothing is currently the state-of-the-art method that provides certified robustness for deep neural networks. However, it often cannot achieve an adequate certified region on real-world datasets. One way to obtain a larger certified region is to use an input-specific algorithm instead of using a fixed Gaussian filter for all data points. Several methods based on this idea have been proposed, but they either suffer from high computational costs or gain marginal improvement in certified radius. In this work, we show that by exploiting the quasiconvex problem structure, we can find the optimal certified radii for most data points with slight computational overhead. This observation leads to an efficient and effective input-specific randomized smoothing algorithm. We conduct extensive experiments and empirical analysis on Cifar10 and ImageNet. The results show that the proposed method significantly enhances the certified radii with low computational overhead.