Generalised Lipschitz Regularisation Equals Distributional Robustness
Generalised Lipschitz Regularisation Equals Distributional Robustness
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发表时间：
2020-02
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通讯作者：
Zac Cranko;Zhan Shi;Xinhua Zhang;R. Nock;Simon Kornblith
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作者：
Zac Cranko;Zhan Shi;Xinhua Zhang;R. Nock;Simon Kornblith
对抗性例子的问题突出了对正则化理论的需要，该理论足够普遍以适用于奇异函数类，例如通用逼近器。作为回应，我们给出了一个非常普遍的平等结果之间的关系分布的鲁棒性和正规化，定义与运输成本的不确定性集。该理论使我们能够（严格）证明Lipschitz正则化模型的鲁棒性，具有非常温和的假设。作为理论应用，我们展示了一个新的结果，解释了对抗学习和分布式鲁棒性之间的联系。然后，我们给出了新的结果，如何实现Lipschitz正则化的内核分类器，这是实验证明。
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.