Optimizing Loss Functions Through Multivariate Taylor Polynomial Parameterization
This work addresses the challenge of improving training efficiency and regularization for deep learning tasks, especially with limited data, though it is incremental as it builds on existing metalearning methods.
The paper tackled the problem of optimizing loss functions for deep neural networks using a continuous CMA-ES approach with multivariate Taylor polynomial parameterizations, resulting in new loss functions that outperform previous genetic programming methods and standard cross-entropy on MNIST, CIFAR-10, and SVHN benchmarks in fewer generations.
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.