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：控制变量是降低蒙特卡洛估计方差的强大工具，但当样本数量较少时，构建有效的控制变量可能具有挑战性。在本文中，我们表明，当需要计算大量相关积分时，即使每个任务的样本数量非常少，也可以利用这些积分任务之间的相似性来提升性能。我们的方法称为元学习控制变量（Meta-CVs），可用于处理多达数百或数千个任务。实证评估表明，在此类设置下，Meta-CVs能够显著降低方差；我们的理论分析则建立了Meta-CVs成功训练的通用条件。