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

• URL: http://arxiv.org/abs/2308.00556v1
• Date: Tue, 1 Aug 2023 13:55:45 GMT
• Title: Robust Linear Regression: Phase-Transitions and Precise Tradeoffs for General Norms
• Authors: Elvis Dohmatob, Meyer Scetbon
• Abstract summary: We investigate the impact of test-time adversarial attacks on linear regression models. We determine the optimal level of robustness that any model can reach while maintaining a given level of standard predictive performance (accuracy) 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.
• Score: 29.936005822346054
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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