Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling

arXiv:2610.16248v1 Announce Type: new Abstract: We study sampling from pi(x)proptoe^{-V(x)} on R^d, where V is alpha-strongly convex and eta-smooth with condition number kappa=eta/alpha. For this problem, the proximal sampler preserves the target exactly and recovers overdamped Langevin dynamics in the small-step limit, but its Gaussian resampling step discards directional information. Underdamped Langevin dynamics retains such information through momentum to accelerate exploration, motivating a proximal construction that combines target preservation with directional persistence. We introduce extit{reflected proximal dynamics}, which combines proximal sampling with an exact reflection of the auxiliary variable, conditional kinetic motion, and controlled refreshment. We develop two realizations: a flux-resampled underdamped half-turn and a persistent-momentum quarter-turn. From a warm start with constant hi^2 divergence, both methods achieve total variation error arepsilon using widetilde O(sqrt{kappa}d^{1/4}) expected oracle queries. We further remove the supplied warm-start assumption by combining either sampler with existing posterior samplers in a proximal initialization stage with an optimized coarse step size. Accounting for both initialization and sampling yields widetilde O(kappa^{6/7}d^{1/4}) expected oracle queries. In both regimes, the dependence on the target accuracy arepsilon is polylog(1/arepsilon), making reflected proximal dynamics a promising framework for accelerated high-accuracy log-concave sampling.

Related

• Accelerated High-Accuracy Sampling from a Warm Start via the Proximal Bouncy Particle Sampler
• Windowed thinning and query complexity for the bouncy particle and Zigzag samplers
• High-accuracy log-concave sampling with stochastic queries

Source: arXiv cs.LG | 2026-10-14