  Extensive empirical evidence reveals that, for a wide range of different
learning 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 linear
classification models and showed that the test error of gradient descent (GD)
with logistic loss undergoes a DD. In this paper, we complement these results
by extending them to GD with square loss. We show that the DD phenomenon
persists, but we also identify several differences compared to logistic loss.
This emphasizes that crucial features of DD curves (such as their transition
threshold and global minima) depend both on the training data and on the
learning algorithm. We further study the dependence of DD curves on the size of
the training set. Similar to our earlier work, our results are analytic: we
plot the DD curves by first deriving sharp asymptotics for the test error under
Gaussian features. Albeit simple, the models permit a principled study of DD
features, the outcomes of which theoretically corroborate related empirical
findings occurring in more complex learning tasks.
