  The risk of overparameterized models, in particular deep neural networks, is
often double-descent shaped as a function of the model size. Recently, it was
shown that the risk as a function of the early-stopping time can also be
double-descent shaped, and this behavior can be explained as a super-position
of bias-variance tradeoffs. In this paper, we show that the risk of explicit
L2-regularized models can exhibit double descent behavior as a function of the
regularization strength, both in theory and practice. We find that for linear
regression, a double descent shaped risk is caused by a superposition of
bias-variance tradeoffs corresponding to different parts of the model and can
be mitigated by scaling the regularization strength of each part appropriately.
Motivated by this result, we study a two-layer neural network and show that
double descent can be eliminated by adjusting the regularization strengths for
the first and second layer. Lastly, we study a 5-layer CNN and ResNet-18
trained on CIFAR-10 with label noise, and CIFAR-100 without label noise, and
demonstrate that all exhibit double descent behavior as a function of the
regularization strength.
