Generalised Lipschitz Regularisation Equals Distributional Robustness
Abstract
The problem of adversarial examples has highlighted the need for a theory of regularisation that is general enough to apply to exotic function classes, such as universal approximators. In response, we give a very general equality result regarding the relationship between distributional robustness and regularisation, as defined with a transportation cost uncertainty set. The theory allows us to (tightly) certify the robustness properties of a Lipschitz-regularised model with very mild assumptions. As a theoretical application we show a new result explicating the connection between adversarial learning and distributional robustness. We then give new results for how to achieve Lipschitz regularisation of kernel classifiers, which are demonstrated experimentally.
Cite
@article{arxiv.2002.04197,
title = {Generalised Lipschitz Regularisation Equals Distributional Robustness},
author = {Zac Cranko and Zhan Shi and Xinhua Zhang and Richard Nock and Simon Kornblith},
journal= {arXiv preprint arXiv:2002.04197},
year = {2020}
}