Meta-learning Control Variates: Variance Reduction with Limited Data
Meta-learning Control Variates: Variance Reduction with Limited Data
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DOI：
10.48550/arxiv.2303.04756
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发表时间：
2023-03
期刊：
影响因子：
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通讯作者：
Z. Sun;C. Oates;F. Briol
中科院分区：
文献类型：
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作者：
Z. Sun;C. Oates;F. Briol
控制变量可以是减少蒙特卡罗估计器方差的强大工具，但是当样本数量很少时，构造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小，也可以利用这些集成任务之间的相似性来提高性能。我们的方法，称为元学习简历（meta - cv），可用于多达数百或数千个任务。我们的经验评估表明，在这种情况下，meta - cv可以显著减少方差，我们的理论分析建立了meta - cv可以成功训练的一般条件。
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.