Deep Neural Networks (DNNs) are often vulnerable to adversarial
examples.Several proposed defenses deploy an ensemble of models with the hope
that, although the individual models may be vulnerable, an adversary will not
be able to find an adversarial example that succeeds against the ensemble.
Depending on how the ensemble is used, an attacker may need to find a single
adversarial example that succeeds against all, or a majority, of the models in
the ensemble. The effectiveness of ensemble defenses against strong adversaries
depends on the vulnerability spaces of models in the ensemble being disjoint.
We consider the joint vulnerability of an ensemble of models, and propose a
novel technique for certifying the joint robustness of ensembles, building upon
prior works on single-model robustness certification. We evaluate the
robustness of various models ensembles, including models trained using
cost-sensitive robustness to be diverse, to improve understanding of the
potential effectiveness of ensemble models as a defense against adversarial
examples.