改进随机中点方法，采样效率比传统方法快3倍。
Poisson Midpoint Method for Log Concave Sampling: Beyond the Strong Error Lower Bounds
- 用泊松中点离散化加速朗之万动力学采样。
- 在2-Wasserstein距离下达到ε精度，复杂度为ε⁻³。
- 适用于高维强对数凹分布采样，尤其适合优化需求高的场景。
研究在ℝᵈ上通过泊松中点离散化（随机中点法的一种变体）对过阻尼/欠阻尼朗之万动力学进行强对数凹分布采样。证明了其在2-Wasserstein距离（W₂）下的收敛性，相比欧拉-马鲁雅玛离散化，目标精度ε的依赖关系实现三次方加速，超越现有随机中点方法的已有界限。值得注意的是，在欠阻尼朗之万动力学情况下，其W₂收敛复杂度远低于文献中关于L²强误差收敛的复杂度下界。
原文摘要 · Abstract (English)
We study the problem of sampling from strongly log-concave distributions over $\mathbb{R}^d$ using the Poisson midpoint discretization (a variant of the randomized midpoint method) for overdamped/underdamped Langevin dynamics. We prove its convergence in the 2-Wasserstein distance ($W_2$), achieving a cubic speedup in dependence on the target accuracy ($ε$) over the Euler-Maruyama discretization, surpassing existing bounds for randomized midpoint methods. Notably, in the case of underdamped Langevin dynamics, we demonstrate the complexity of $W_2$ convergence is much smaller than the complexity lower bounds for convergence in $L^2$ strong error established in the literature.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。