Geometric ergodicity of SGLD via reflection coupling
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Abstract (arXiv)
We consider the geometric ergodicity of the Stochastic Gradient Langevin Dynamics (SGLD) algorithm under nonconvexity settings. Via the technique of reflection coupling, we prove the Wasserstein contraction of SGLD when the target distribution is log-concave only outside some compact set. The time discretization and the minibatch in SGLD introduce several difficulties when applying the reflection coupling, which are addressed by a series of careful estimates of conditional expectations. As a direct corollary, the SGLD with constant step size has an invariant distribution and we are able to obtain its geometric ergodicity in terms of W1 distance. The generalization to non-gradient drifts is also included.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 8 of its 33 references that are in the map. First posted on arXiv 17 Jan 2023.
Builds on
8 of 33 references.
References · 8
- 2017Generalization Bounds of SGLD for Non-convex Learning: Two Theoretical Viewpointscited by 82
- 2018The promises and pitfalls of Stochastic Gradient Langevin Dynamicscited by 56
- 2019Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimizationcited by 38
- 2018Coupling and Convergence for Hamiltonian Monte Carlocited by 36
- 2018Non-asymptotic bounds for sampling algorithms without log-concavitycited by 35
- 2020Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Samplingcited by 32
- 2021Time-independent Generalization Bounds for SGLD in Non-convex Settingscited by 27
- 2022A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamicscited by 3
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Citing papers per year: 2023: 1.
1 paper.
- 2023Subsampling Error in Stochastic Gradient Langevin Diffusions23 May 2023