  We consider a family of unadjusted generalized HMC samplers, which includes
standard position HMC samplers and discretizations of the underdamped Langevin
process. A detailed analysis and optimization of the parameters is conducted in
the Gaussian case, which shows an improvement from $1/\kappa$ to
$1/\sqrt{\kappa}$ for the convergence rate in terms of the condition number
$\kappa$ by using partial velocity refreshment, with respect to classical full
refreshments. A similar effect is observed empirically for two related
algorithms, namely Metropolis-adjusted gHMC and kinetic piecewise-deterministic
Markov processes. Then, a stochastic gradient version of the samplers is
considered, for which dimension-free convergence rates are established for
log-concave smooth targets over a large range of parameters, gathering in a
unified framework previous results on position HMC and underdamped Langevin and
extending them to HMC with inertia.
