Malign Overfitting: Interpolation and Invariance are Fundamentally at Odds
Keywords: Invariance, Overparameterization, Fairness, Robustness, Benign Overfitting
TL;DR: Proof that interpolating classifiers cannot satisfy common invariance and fairness criteria; Provides insight on empirical observations and possible effective solutions
Abstract: Learned classifiers should often possess certain invariance properties meant to encourage fairness, robustness, or out-of-distribution generalization.
However, multiple recent works empirically demonstrate that common invariance-inducing regularizers are ineffective in the over-parameterized regime, in which classifiers perfectly fit (i.e. interpolate) the training data. This suggests that the phenomenon of ``benign overfitting," in which models generalize well despite interpolating, might not favorably extend to settings in which robustness or fairness are desirable.
In this work, we provide a theoretical justification for these observations. We prove that---even in the simplest of settings---any interpolating learning rule (with an arbitrarily small margin) will not satisfy these invariance properties. We then propose and analyze an algorithm that---in the same setting---successfully learns a non-interpolating classifier that is provably invariant. We validate our theoretical observations on simulated data and the Waterbirds dataset.
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