A Novel Plug-and-Play Approach for Adversarially Robust Generalization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866910709364817920 |
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| author | Maurya, Deepak Barik, Adarsh Honorio, Jean |
| author_facet | Maurya, Deepak Barik, Adarsh Honorio, Jean |
| contents | In this work, we propose a robust framework that employs adversarially robust training to safeguard the ML models against perturbed testing data. Our contributions can be seen from both computational and statistical perspectives. Firstly, from a computational/optimization point of view, we derive the ready-to-use exact solution for several widely used loss functions with a variety of norm constraints on adversarial perturbation for various supervised and unsupervised ML problems, including regression, classification, two-layer neural networks, graphical models, and matrix completion. The solutions are either in closed-form, or an easily tractable optimization problem such as 1-D convex optimization, semidefinite programming, difference of convex programming or a sorting-based algorithm. Secondly, from statistical/generalization viewpoint, using some of these results, we derive novel bounds of the adversarial Rademacher complexity for various problems, which entails new generalization bounds. Thirdly, we perform some sanity-check experiments on real-world datasets for supervised problems such as regression and classification, as well as for unsupervised problems such as matrix completion and learning graphical models, with very little computational overhead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09449 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Novel Plug-and-Play Approach for Adversarially Robust Generalization Maurya, Deepak Barik, Adarsh Honorio, Jean Machine Learning In this work, we propose a robust framework that employs adversarially robust training to safeguard the ML models against perturbed testing data. Our contributions can be seen from both computational and statistical perspectives. Firstly, from a computational/optimization point of view, we derive the ready-to-use exact solution for several widely used loss functions with a variety of norm constraints on adversarial perturbation for various supervised and unsupervised ML problems, including regression, classification, two-layer neural networks, graphical models, and matrix completion. The solutions are either in closed-form, or an easily tractable optimization problem such as 1-D convex optimization, semidefinite programming, difference of convex programming or a sorting-based algorithm. Secondly, from statistical/generalization viewpoint, using some of these results, we derive novel bounds of the adversarial Rademacher complexity for various problems, which entails new generalization bounds. Thirdly, we perform some sanity-check experiments on real-world datasets for supervised problems such as regression and classification, as well as for unsupervised problems such as matrix completion and learning graphical models, with very little computational overhead. |
| title | A Novel Plug-and-Play Approach for Adversarially Robust Generalization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2208.09449 |