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Structured second-order methods via natural gradient descent

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arxiv 2107.10884 v3 pith:PDLUECTY submitted 2021-07-22 stat.ML cs.LG

Wu Lin , Frank Nielsen , Mohammad Emtiyaz Khan , Mark Schmidt This is my paper
classification stat.MLcs.LG
keywords methodsstructureddescentsecond-orderadaptive-gradientnatural-gradientproblemsadmit
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In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to design new algorithms in many settings such as gradient-free, adaptive-gradient, and second-order methods. Our structured methods not only enjoy a structural invariance but also admit a simple expression. Finally, we test the efficiency of our proposed methods on both deterministic non-convex problems and deep learning problems.

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  1. Optimization Guarantees for Square-Root Natural-Gradient Variational Inference

    cs.LG 2025-07 conditional novelty 7.0 of 10

    For strongly concave log-likelihoods, square-root (Cholesky) parametrization of Gaussian variational inference yields exponential convergence guarantees for both the natural-gradient flow and a discrete-time natural-g...

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