Loss-function metalearning can be used to discover novel, customized loss functions for deep neural networks, resulting in improved performance, faster training, and improved data utilization. A likely explanation is that such functions discourage overfitting, leading to effective regularization. This paper theoretically demonstrates that this is indeed the case: decomposition of learning rules makes it possible to characterize the training dynamics and show that loss functions evolved through TaylorGLO regularize both in the beginning and end of learning, and maintain an invariant in between. The invariant can be utilized to make the metalearning process more efficient in practice, and the regularization can train networks that are robust against adversarial attacks. Loss-function optimization can thus be seen as a well-founded new aspect of metalearning in neural networks.

As the complexity of neural network models has grown, it has become increasingly important to optimize their design automatically through metalearning. Methods for discovering hyperparameters, topologies, and learning rate schedules have lead to significant increases in performance. This paper shows that loss functions can be optimized with metalearning as well, and result in similar improvements. The method, Genetic Loss-function Optimization (GLO), discovers loss functions de novo, and optimizes them for a target task. Leveraging techniques from genetic programming, GLO builds loss functions hierarchically from a set of operators and leaf nodes. These functions are repeatedly recombined and mutated to find an optimal structure, and then a covariance-matrix adaptation evolutionary strategy (CMA-ES) is used to find optimal coefficients. Networks trained with GLO loss functions are found to outperform the standard cross-entropy loss on standard image classification tasks. Training with these new loss functions requires fewer steps, results in lower test error, and allows for smaller datasets to be used. Loss-function optimization thus provides a new dimension of metalearning, and constitutes an important step towards AutoML.