# Generalised Lipschitz Regularisation Equals Distributional Robustness

arXiv: https://arxiv.org/abs/2002.04197 · HTML: https://mlsanity.com/paper/2002.04197/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2020.

## Built on by (most cited first, 14 of 14)

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- [Certifying Out-of-Domain Generalization for Blackbox Functions](https://mlsanity.com/paper/2202.01679/) (2022)
- [Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints](https://mlsanity.com/paper/2210.01413/) (2022)
- [On Certifying and Improving Generalization to Unseen Domains](https://mlsanity.com/paper/2206.12364/) (2022)
- [A direct proof of a unified law of robustness for Bregman divergence losses](https://mlsanity.com/paper/2405.16639/) (2024)
- [Achieving Domain-Independent Certified Robustness via Knowledge Continuity](https://mlsanity.com/paper/2411.01644/) (2024)
- [Distributionally Robust Skeleton Learning of Discrete Bayesian Networks](https://mlsanity.com/paper/2311.06117/) (2023)
- [Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness](https://mlsanity.com/paper/2509.26275/) (2025)
- [Generalization Analysis and Method for Domain Generalization for a Family of Recurrent Neural Networks](https://mlsanity.com/paper/2601.08122/) (2026)

## Abstract (arXiv)

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.