A Fundamental Accuracy--Robustness Trade-off in Regression and Classification

Sohail Bahmani

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arXiv · 2411.05853

A Fundamental Accuracy--Robustness Trade-off in Regression and Classification

Sohail Bahmani

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Abstract

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. Generalizing our analysis of this example, we formulate a necessary condition under which adversarial robustness can be achieved without significant degradation of the accuracy. This necessary condition is expressed in terms of a quantity that resembles the Poincar\'{e} constant of the data distribution.

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Sohail Bahmani. 2024-11-06. A Fundamental Accuracy--Robustness Trade-off in Regression and Classification. https://arxiv.org/abs/2411.05853

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