Coupling and Convergence for Hamiltonian Monte Carlo

Understand

Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t.

• a carefully designed Kantorovich (L1 Wasserstein) distance.
• The lower bound for the contraction rate is explicit.
• Global convexity of the potential is not required, and thus multimodal target distributions are included.