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：控制变量法可以成为降低蒙特卡洛估计量方差的有力工具，但当样本数量较少时，构建有效的控制变量可能颇具挑战。本文表明，在需要计算大量相关积分的情况下，即使每个任务的样本数量非常少，也可通过利用这些积分任务之间的相似性来提升性能。我们提出的方法称为元学习控制变量法（Meta-CVs），可适用于数百甚至数千个任务。实验评估表明，在此类场景下，Meta-CVs能够实现显著的方差缩减；而理论分析则建立了Meta-CVs可成功训练的通用条件。