Control variates can be a powerful tool to reduce the variance of Monte Carlo estimators, but constructing effective control variates can be challenging when the number of samples is small. In this paper, we show that when a large number of related integrals need to be computed, it is possible to leverage the similarity between these integration tasks to improve performance even when the number of samples per task is very small. Our approach, called meta learning CVs (Meta-CVs), can be used for up to hundreds or thousands of tasks. Our empirical assessment indicates that Meta-CVs can lead to significant variance reduction in such settings, and our theoretical analysis establishes general conditions under which Meta-CVs can be successfully trained.
翻译:控制变量可以是减少蒙特卡洛估计值差异的有力工具,但当样本数量少时,建立有效的控制变量会具有挑战性。 在本文中,我们表明,当需要计算大量相关整体体时,即使每个任务样本数量很少,也可以利用这些整合任务之间的相似性来提高性能。我们的方法,即所谓的元学习CV(Meta-CVs),可以用于多达数百或数千项任务。我们的经验评估表明,Meta-CV可以导致这种环境中差异的显著减少,我们的理论分析确定了可以成功培训Meta-CV的一般条件。</s>