  Randomized Smoothing (RS) is a promising method for obtaining robustness
certificates by evaluating a base model under noise. In this work, we: (i)
theoretically motivate why ensembles are a particularly suitable choice as base
models for RS, and (ii) empirically confirm this choice, obtaining
state-of-the-art results in multiple settings. The key insight of our work is
that the reduced variance of ensembles over the perturbations introduced in RS
leads to significantly more consistent classifications for a given input. This,
in turn, leads to substantially increased certifiable radii for samples close
to the decision boundary. Additionally, we introduce key optimizations which
enable an up to 55-fold decrease in sample complexity of RS for predetermined
radii, thus drastically reducing its computational overhead. Experimentally, we
show that ensembles of only 3 to 10 classifiers consistently improve on their
strongest constituting model with respect to their average certified radius
(ACR) by 5% to 21% on both CIFAR10 and ImageNet, achieving a new
state-of-the-art ACR of 0.86 and 1.11, respectively. We release all code and
models required to reproduce our results at
https://github.com/eth-sri/smoothing-ensembles.
