Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling
We study sampling from $π(x)\propto\mathrm{e}^{-V(x)}$ on $\mathbb{R}^d$, where $V$ is $α$-strongly convex and $β$-smooth with condition number $κ=β/α$. 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 \textit{reflected proximal dynamics}, which combines proximal sampling with an exact reflection of the auxiliary variable, conditio...
| Authors | Bo Yuan, Wei Guo, Yongxin Chen |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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