Acceleration and its Limits in Gaussian Variational Inference
We study whether the classical momentum-based acceleration that improves the condition-number dependence of gradient descent from $κ$ to $\sqrtκ$ for strongly convex, smooth objectives extends to Gaussian variational inference (GVI) for strongly log-concave, log-smooth target distributions. With exact Gaussian expectations, a convex composite formulation of GVI yields the classical accelerated $\sqrtκ$ convergence rate. However, when only pointwise derivatives are available, we construct a family of strongly log-concave targets for which any randomized algorithm requires $κ^{1-o(1)}$ queries to achieve a fixed objective accuracy, even when the initial objective gap is bounded independentl...
| Authors | Jaesung R. Park, Uijeong Jang, Yifan Chen |
|---|---|
| Primary category | stat.ML |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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