# Generalized Optimization: A First Step Towards Category Theoretic Learning Theory

@inproceedings{Shiebler2021GeneralizedOA, title={Generalized Optimization: A First Step Towards Category Theoretic Learning Theory}, author={Dan Shiebler}, booktitle={ICO}, year={2021} }

The Cartesian reverse derivative is a categorical generalization of reverse-mode automatic differentiation. We use this operator to generalize several optimization algorithms, including a straightforward generalization of gradient descent and a novel generalization of Newton's method. We then explore which properties of these algorithms are preserved in this generalized setting. First, we show that the transformation invariances of these algorithms are preserved: while generalized Newton's…

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