Belangrijkste concepten
The study proves the convergence of Kinetic Langevin dynamics on Lie groups with explicit rates under W2 distance.
Samenvatting
The study introduces a novel Lie-group MCMC sampler based on kinetic Langevin dynamics. It provides rigorous and quantitative analysis of geometric ergodicities, showcasing exponential convergence without requiring convexity or isoperimetry. The paper also discusses the challenges of sampling on manifolds and presents results for optimization dynamics on Riemannian manifolds. The discretization technique used in the algorithm ensures structure preservation, eliminating the need for additional projection back to the manifold. The error bounds for both continuous and discrete samplers are proven under specific assumptions about the Lie group and potential function smoothness.
Statistieken
Exponential convergence is proved under W2 distance.
Only compactness of the Lie group and geodesically L-smoothness of the potential function are needed.
The nonasymptotic error bound for the sampler in discrete time is provided.