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Extensive empirical evidence reveals that, for a wide range of differentlearning methods and datasets, the risk curve exhibits a double-descent (DD)trend as a function of the model size. In a recent paper[Zeyu,Kammoun,Thrampoulidis,2019] the authors studied binary linearclassification models and showed that the test error of gradient descent (GD)with logistic loss undergoes a DD. In this paper, we complement these resultsby extending them to GD with square loss. We show that the DD phenomenonpersists, but we also identify several differences compared to logistic loss.This emphasizes that crucial features of DD curves (such as their transitionthreshold and global minima) depend both on the training data and on thelearning algorithm. We further study the dependence of DD curves on the size ofthe training set. Similar to our earlier work, our results are analytic: weplot the DD curves by first deriving sharp asymptotics for the test error underGaussian features. Albeit simple, the models permit a principled study of DDfeatures, the outcomes of which theoretically corroborate related empiricalfindings occurring in more complex learning tasks.

Analytic Study of Double Descent in Binary Classification: The Impact of Loss