Importantly, our rates are optimistic, i.e., they interpolate

Rounding out the story and contributions, firstly we present a brief toy univariate model hinting towards the necessity of early stopping: concretely, any univariate predictor satisfying alocal interpolation propertycan not achieve optimal test error for noisy distributions.

Whilestochastic optimization ofAUROChasbeenstudied extensively, principled stochastic optimization of AUPRC has been rarely explored.