We explore the sampling problem within the framework where parallel evaluations of the gradient of the log-density are feasible. Our investigation focuses on target distributions characterized by smooth and strongly log-concave densities. We revisit the parallelized randomized midpoint method and employ proof techniques recently developed for analyzing its purely sequential version. Leveraging these techniques, we derive upper bounds on the Wasserstein distance between the sampling and target densities. These bounds quantify the runtime improvement achieved by utilizing parallel processing units, which can be considerable.

翻译：我们探讨在可并行计算对数密度梯度框架下的采样问题。研究聚焦于具有光滑且强对数凹性质的密度所刻画的目标分布。我们重新审视了并行化随机中点方法，并采用近期为分析其纯序列版本而发展的证明技术。借助这些技术，我们推导出采样密度与目标密度之间Wasserstein距离的上界。这些上界量化了利用并行处理单元所实现的运行时间提升，该提升幅度相当可观。