模型鲁棒性与准确率存在根本权衡，平滑性不足是关键原因。
A Fundamental Accuracy--Robustness Trade-off in Regression and Classification
- 基于数据分布的平滑性分析，揭示鲁棒性与准确率的内在矛盾。
- 在多项式岭回归中验证了该权衡，证明非光滑预测器无法兼顾两者。
- 提出实现鲁棒性而不降准的必要条件，关联数据分布的Poincaré常数。
我们在一个较为一般的情形下推导出标准风险与对抗风险之间的根本性权衡，其背后直观原理是：若不存在（近似）最优且平滑的预测器，则对抗鲁棒性必然以牺牲准确性为代价。以满足弱正则性条件的多项式岭回归为例，我们评估了这一权衡关系。通过推广该例证的分析，我们提出了实现对抗鲁棒性而无需显著降低准确性的必要条件，该条件以类似数据分布的Poincaré常数的量来表达。
原文摘要 · Abstract (English)
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 Poincaré constant of the data distribution.
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