Smoothed Picard Hamiltonian Monte Carlo

arXiv:2609.06906v1 Announce Type: cross Abstract: We develop a new low-accuracy sampler, called smoothed Picard Hamiltonian Monte Carlo, which combines Gaussian smoothing, Picard iteration, and higher-order discretization. For a log-concave target pi propto exp(-V) in dimension d satisfying 0 prec alpha I preceq nabla^2 V preceq eta I, with condition number kappa := eta/alpha, smoothed Picard HMC returns a sample with sqrt alpha,W_2(dot,pi) le arepsilon using widetilde O(kappa^2 + kappa^{7/6} d^{1/6}/arepsilon^{1/3}) gradient queries. We also prove stronger W_q bounds, and then develop an algorithmic framework, the recursive warm start generator, to upgrade these W_q bounds to stronger divergence guarantees. This produces a warm start for the proximal bouncy particle sampler, introduced in a companion work, leading to a high-accuracy log-concave sampler with complexity widetilde O((kappa^{7/6} d^{1/6} + kappa^{1/2} d^{1/4})polylog(1/arepsilon)).

Source: arXiv cs.LG | 2026-09-09