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arXiv · 2102.07405

Tractable structured natural gradient descent using local parameterizations

Wu Lin·Frank Nielsen·Mohammad Emtiyaz Khan·Mark Schmidt
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Abstract

Natural-gradient descent (NGD) on structured parameter spaces (e.g., low-rank covariances) is computationally challenging due to difficult Fisher-matrix computations. We address this issue by using \emph{local-parameter coordinates} to obtain a flexible and efficient NGD method that works well for a wide-variety of structured parameterizations. We show four applications where our method (1) generalizes the exponential natural evolutionary strategy, (2) recovers existing Newton-like algorithms, (3) yields new structured second-order algorithms via matrix groups, and (4) gives new algorithms to learn covariances of Gaussian and Wishart-based distributions. We show results on a range of problems from deep learning, variational inference, and evolution strategies. Our work opens a new direction for scalable structured geometric methods.

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Wu Lin, Frank Nielsen, Mohammad Emtiyaz Khan, Mark Schmidt. 2022-01-17. Tractable structured natural gradient descent using local parameterizations. https://arxiv.org/abs/2102.07405

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