  The benefits of overparameterization for the overall performance of modern
machine learning (ML) models are well known. However, the effect of
overparameterization at a more granular level of data subgroups is less
understood. Recent empirical studies demonstrate encouraging results: (i) when
groups are not known, overparameterized models trained with empirical risk
minimization (ERM) perform better on minority groups; (ii) when groups are
known, ERM on data subsampled to equalize group sizes yields state-of-the-art
worst-group-accuracy in the overparameterized regime. In this paper, we
complement these empirical studies with a theoretical investigation of the risk
of overparameterized random feature models on minority groups. In a setting in
which the regression functions for the majority and minority groups are
different, we show that overparameterization always improves minority group
performance.
