Robust Linear Regression: Phase-Transitions and Precise Tradeoffs for General Norms

Elvis Dohmatob; Meyer Scetbon

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arXiv · 2308.00556

Robust Linear Regression: Phase-Transitions and Precise Tradeoffs for General Norms

Elvis Dohmatob·Meyer Scetbon

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Abstract

In this paper, we investigate the impact of test-time adversarial attacks on linear regression models and determine the optimal level of robustness that any model can reach while maintaining a given level of standard predictive performance (accuracy). Through quantitative estimates, we uncover fundamental tradeoffs between adversarial robustness and accuracy in different regimes. We obtain a precise characterization which distinguishes between regimes where robustness is achievable without hurting standard accuracy and regimes where a tradeoff might be unavoidable. Our findings are empirically confirmed with simple experiments that represent a variety of settings. This work applies to feature covariance matrices and attack norms of any nature, and extends beyond previous works in this area.

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BibTeX RIS

Elvis Dohmatob, Meyer Scetbon. 2023-08-01. Robust Linear Regression: Phase-Transitions and Precise Tradeoffs for General Norms. https://arxiv.org/abs/2308.00556

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