Benign Overfitting and Double Descent

This talk is an addendum to a talk on "Benign overfitting in linear regression" (joint with Phil Long, Gabor Lugosi and Alex Tsigler) in the program's first workshop. That work investigated the phenomenon of overfitting prediction rules that predict accurately by considering a simple setting, that of linear prediction, and gave a characterization of linear regression problems for which the minimum norm interpolating prediction rule has near-optimal prediction accuracy. This talk presents some consequences, showing that there can be a rich variety of possible behaviors of excess risk as a function of dimension.