Theoretical guarantees for stochastic gradient sampling methods via Gaussian convolution inequalities
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917440317816832 |
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| author | Paulin, Daniel Whalley, Peter A. |
| author_facet | Paulin, Daniel Whalley, Peter A. |
| contents | We derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptions on the stochastic gradient noise. These bounds sharpen existing non-asymptotic guarantees for stochastic-gradient MCMC methods and provide a quantitative resolution of a previously open problem on invariant measure accuracy. The main technical ingredients are new Gaussian convolution inequalities controlling the Wasserstein-$p$ distance between a Gaussian convolved with a mean-zero perturbation and the Gaussian itself. We anticipate that these inequalities will be of independent interest beyond the present application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24632 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Theoretical guarantees for stochastic gradient sampling methods via Gaussian convolution inequalities Paulin, Daniel Whalley, Peter A. Computation Numerical Analysis Probability 65C05, 65C30, 65C40 We derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptions on the stochastic gradient noise. These bounds sharpen existing non-asymptotic guarantees for stochastic-gradient MCMC methods and provide a quantitative resolution of a previously open problem on invariant measure accuracy. The main technical ingredients are new Gaussian convolution inequalities controlling the Wasserstein-$p$ distance between a Gaussian convolved with a mean-zero perturbation and the Gaussian itself. We anticipate that these inequalities will be of independent interest beyond the present application. |
| title | Theoretical guarantees for stochastic gradient sampling methods via Gaussian convolution inequalities |
| topic | Computation Numerical Analysis Probability 65C05, 65C30, 65C40 |
| url | https://arxiv.org/abs/2604.24632 |