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arXiv · 2507.07853

Optimization Guarantees for Square-Root Natural-Gradient Variational Inference

Navish Kumar·Thomas Möllenhoff·Mohammad Emtiyaz Khan·Aurelien Lucchi
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Abstract

Variational inference with natural-gradient descent often shows fast convergence in practice, but its theoretical convergence guarantees have been challenging to establish. This is true even for the simplest cases that involve concave log-likelihoods and use a Gaussian approximation. We show that the challenge can be circumvented for such cases using a square-root parameterization for the Gaussian covariance. This approach establishes novel convergence guarantees for natural-gradient variational-Gaussian inference and its continuous-time gradient flow. Our experiments demonstrate the effectiveness of natural gradient methods and highlight their advantages over algorithms that use Euclidean or Wasserstein geometries.

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Navish Kumar, Thomas Möllenhoff, Mohammad Emtiyaz Khan, Aurelien Lucchi. 2025-07-10. Optimization Guarantees for Square-Root Natural-Gradient Variational Inference. https://arxiv.org/abs/2507.07853

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