Reflective Hamiltonian Monte Carlo: Mixing Analysis and Application to Sampling on Stiefel Manifold

Sampling from distributions with bounded supports is a fundamental challenge in constrained statistical inference. Reflective Hamiltonian Monte Carlo (ReHMC) provides a useful approach for this setting, but relies on convexity assumptions and lacks non-asymptotic mixing-time bounds. To bridge this gap, we propose a convex-container-plus-thinning framework that extends ReHMC beyond smooth convex supports to a broad class of bounded supports. We establish the first non-asymptotic total-variation mixing-time bounds for ReHMC, achieving a polynomial dimension dependence of $O(d^2)$ for $L$-smooth targets, though with exponential dependence on smoothness parameters. Under an additional $m$-strong convexity assumption, we derive a sharper bound that eliminates this exponential dependence. We further apply this approach to sampling on the Stiefel manifold via a well-conditioned polar reparameterization and demonstrate improved numerical stability and computational efficiency in simulation studies.

In Proceedings of the 43rd International Conference on Machine Learning