论文标题
通过Mirror-Langevin算法有效地约束采样
Efficient constrained sampling via the mirror-Langevin algorithm
论文作者
论文摘要
我们提出了镜像扩散的新离散化，并给出了清晰的融合证明。我们的分析使用了相对凸度/平滑度和自我符合的想法，这些想法起源于凸优化，以及最佳运输的新结果，从而概括了熵的位移凸度。与先前的工作不同，我们的结果（1）都需要在镜像图和目标分布上的假设较弱，并且（2）随着步长的趋势趋于零而消失了偏差。特别是，对于从紧凑型集合支持的对数孔分布进行采样的任务时，我们的理论结果明显优于现有保证。
We propose a new discretization of the mirror-Langevin diffusion and give a crisp proof of its convergence. Our analysis uses relative convexity/smoothness and self-concordance, ideas which originated in convex optimization, together with a new result in optimal transport that generalizes the displacement convexity of the entropy. Unlike prior works, our result both (1) requires much weaker assumptions on the mirror map and the target distribution, and (2) has vanishing bias as the step size tends to zero. In particular, for the task of sampling from a log-concave distribution supported on a compact set, our theoretical results are significantly better than the existing guarantees.
