Convergence rates for Langevin Monte Carlo on Riemannian manifolds with non-convex potentials

What the research examines

Provides the first non-asymptotic polynomial convergence bounds for Riemannian Langevin dynamics sampling from target distributions satisfying a Riemannian Poincaré inequality, without requiring uniform geodesic convexity.

Why it may matter

Establishes rigorous computational efficiency bounds for high-dimensional Bayesian inference and manifold learning.

What to examine carefully

Constants depend exponentially on the oscillation of the potential, mirroring fundamental metastability barriers.

Try a small, reproducible follow-up

Implement Riemannian Langevin dynamics on the 2-sphere S^2 for a mixture of von Mises-Fisher distributions and measure Kullback-Leibler divergence decay over iteration steps.

Questions to investigate

1. How is metric connection curvature integrated into the discretization drift-diffusion analysis?
2. What step-size schedule ensures stability when Ricci curvature is negatively bounded?

These are independently proposed educational investigations, not activities that the original research authors claim to have completed.

Publication & researcher information

Multi-author research may involve universities in several countries. Unverified institutions and contact addresses are not inferred from authors' names.

Primary sources