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Tractable structured natural-gradient descent using local parameterizations
Wu Lin · Frank Nielsen · Khan Emtiyaz · Mark Schmidt

Wed Jul 21 06:35 AM -- 06:40 AM (PDT) @ None

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, 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.

Author Information

Wu Lin (University of British Columbia)
Frank Nielsen (Sony CSL, Japan)
Khan Emtiyaz (RIKEN)
Mark Schmidt (University of British Columbia)

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