2604.01416 Hamiltonian Monte Carlo with Dual Averaging Mixes in O(d^{1/4}) Gradient Evaluations for Log-Concave Targets: A Non-Asymptotic Bound
Hamiltonian Monte Carlo (HMC) with dual averaging step size adaptation is the gold standard for sampling continuous distributions, but sharp non-asymptotic mixing time bounds have been elusive. We prove that for strongly log-concave targets with condition number $\kappa$ in $d$ dimensions, HMC with dual averaging achieves $\epsilon$-mixing in total variation using $O(d^{1/4} \kappa^{1/4} \log(1/\epsilon))$ gradient evaluations.