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, 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.
