Optimizing Loss Functions Through Multivariate Taylor Polynomial Parameterization

Santiago Gonzalez, Risto Miikkulainen

Keywords: taylorglo, loss function, metalearning, evolution, deep networks, evolutionary strategies, taylor polynomials, glo

Abstract: 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.

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One-sentence Summary: This paper introduces TaylorGLO, a technique that metalearns loss functions that result in higher performance deep networks.

Reviewed Version (pdf): https://openreview.net/references/pdf?id=37UGiFHRQq