Poster

Adversarially Robust Kernel Smoothing

Jia-Jie Zhu · Christina Kouridi · Yassine Nemmour · Bernhard Schölkopf

Virtual
[ Abstract ]
Wed 30 Mar 3:30 a.m. PDT — 5 a.m. PDT
 
Oral presentation: Oral 5: Kernels / Optimization / Deep learning
Tue 29 Mar 2:30 a.m. PDT — 3:30 a.m. PDT

Abstract:

We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the Wasserstein distance and the maximum mean discrepancy. We adapt the integral operator using supremal convolution in convex analysis to form a novel function majorant used for enforcing robustness. Our method is simple in form and applies to general loss functions and machine learning models. Exploiting a connection with optimal transport, we prove theoretical guarantees for certified robustness under distribution shift. Furthermore, we report experiments with general machine learning models, such as deep neural networks, to demonstrate competitive performance with the state-of-the-art certifiable robust learning algorithms based on the Wasserstein distance.

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