Truncated Log-concave Sampling for Convex Bodies with Reflective Hamiltonian Monte Carlo

We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm, to sample from a log-concave distribution restricted convex body. prove that, starting warm start, the walk mixes target $\pi(x) \propto e^{-f(x)}$, where $f$ is $L$-smooth and $m$-strongly-convex, within accuracy $\varepsilon$ after $\widetilde O(\kappa d^2 \ell^2 \log (1 / \varepsilon))$ steps for well-rounded body $\kappa = L m$ condition number of negative log-density, $d$ dimension, $\ell$ upper bound on reflections, parameter. also developed efficient open source implementation ReHMC we performed experimental study various high-dimensional data-sets. The experiments suggest that outperfroms Hit-and-Run Coordinate-Hit-and-Run regarding time it needs produce independent introduces practical truncated sampling in thousands dimensions.