Tractable structured natural gradient descent using local parameterizations

• URL: http://arxiv.org/abs/2102.07405v1
• Date: Mon, 15 Feb 2021 09:09:20 GMT
• Title: Tractable structured natural gradient descent using local parameterizations
• Authors: Wu Lin, Frank Nielsen, Mohammad Emtiyaz Khan, Mark Schmidt
• Abstract summary: Natural-gradient descent on structured parameter spaces is computationally challenging due to complicated inverse Fisher-matrix computations. We address this issue by using emphlocal- parameter coordinates. We show results on a range of applications on deep learning, variational inference, and evolution strategies.
• Score: 43.51581051770027
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Natural-gradient descent on structured parameter spaces (e.g., low-rank covariances) is computationally challenging due to complicated inverse Fisher-matrix computations. We address this issue for optimization, inference, and search problems by using \emph{local-parameter coordinates}. Our method generalizes an existing evolutionary-strategy method, recovers Newton and Riemannian-gradient methods as special cases, and also yields new tractable natural-gradient algorithms for learning flexible covariance structures of Gaussian and Wishart-based distributions. We show results on a range of applications on deep learning, variational inference, and evolution strategies. Our work opens a new direction for scalable structured geometric methods via local parameterizations.

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