Lipschitz Networks and Distributional Robustness

Understand

Robust risk minimisation has several advantages: it has been studied with regards to improving the generalisation properties of models and robustness to adversarial perturbation.

• We bound the distributionally robust risk for a model class rich enough to include deep neural networks by a regularised empirical risk involving the Lipschitz constant of the model.
• This allows us to interpretand quantify the robustness properties of a deep neural network.
• As an application we show the distributionally robust risk upperbounds the adversarial training risk.