  Metalearning of deep neural network (DNN) architectures and hyperparameters
has become an increasingly important area of research. Loss functions are a
type of metaknowledge that is crucial to effective training of DNNs, however,
their potential role in metalearning has not yet been fully explored. Whereas
early work focused on genetic programming (GP) on tree representations, this
paper proposes continuous CMA-ES optimization of multivariate Taylor polynomial
parameterizations. This approach, TaylorGLO, makes it possible to represent and
search useful loss functions more effectively. In MNIST, CIFAR-10, and SVHN
benchmark tasks, TaylorGLO finds new loss functions that outperform functions
previously discovered through GP, as well as the standard cross-entropy loss,
in fewer generations. These functions serve to regularize the learning task by
discouraging overfitting to the labels, which is particularly useful in tasks
where limited training data is available. The results thus demonstrate that
loss function optimization is a productive new avenue for metalearning.
