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：我们研究在可并行计算对数密度梯度框架下的采样问题。重点考察具有光滑且强对数凹特性的目标分布。我们重新审视并行化随机中点方法，并采用近期为分析其纯串行版本而开发的证明技术。基于这些技术，我们推导出采样密度与目标密度之间Wasserstein距离的上界。这些上界量化了使用并行处理单元所带来的运行时间改进——这种改进可能相当显著。