Paper ID: 2411.05853 • Published Nov 6, 2024
A Fundamental Accuracy--Robustness Trade-off in Regression and Classification
Sohail Bahmani
TL;DR
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We derive a fundamental trade-off between standard and adversarial risk in a
rather general situation that formalizes the following simple intuition: "If no
(nearly) optimal predictor is smooth, adversarial robustness comes at the cost
of accuracy." As a concrete example, we evaluate the derived trade-off in
regression with polynomial ridge functions under mild regularity conditions.