  Variational inference lies at the core of many state-of-the-art algorithms.
To improve the approximation of the posterior beyond parametric families, it
was proposed to include MCMC steps into the variational lower bound. In this
work we explore this idea using steps of the Hamiltonian Monte Carlo (HMC)
algorithm, an efficient MCMC method. In particular, we incorporate the
acceptance step of the HMC algorithm, guaranteeing asymptotic convergence to
the true posterior. Additionally, we introduce some extensions to the HMC
algorithm geared towards faster convergence. The theoretical advantages of
these modifications are reflected by performance improvements in our
experimental results.
