Tractable structured natural gradient descent using local parameterizations

TL;DR

This paper introduces a flexible and efficient natural-gradient descent method using local-parameter coordinates, enabling scalable structured optimization across deep learning, variational inference, and evolution strategies.

Contribution

It presents a novel NGD approach that leverages local-parameterizations to handle various structured parameter spaces efficiently.

Findings

Generalizes exponential natural evolutionary strategies

Recovers existing Newton-like algorithms

Provides new structured second-order algorithms

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.