  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.
