论文标题
一项强大的法律，用于炒净集成
A strong law of large numbers for scrambled net integration
论文作者
论文摘要
本文为在数字网上集成的大量法律提供了强大的定律，该定律是由嵌套统一的争夺随机分配的。激励的问题是在贝叶斯优化中出现的积分的某些整体变量优化。这项强大的法律要求intighand的订单$ p $有限的时刻，以$> 1 $。以前已知的结果暗示仅针对Riemann综合功能的强大定律。以前的大量扰流网的一般弱定律需要正方形的集成集成。我们通过riesz-thorin插值定理从$ l^2 $ to $ l^p $ for $ p> 1 $概括
This article provides a strong law of large numbers for integration on digital nets randomized by a nested uniform scramble. The motivating problem is optimization over some variables of an integral over others, arising in Bayesian optimization. This strong law requires that the integrand have a finite moment of order $p$ for some $p>1$. Previously known results implied a strong law only for Riemann integrable functions. Previous general weak laws of large numbers for scrambled nets require a square integrable integrand. We generalize from $L^2$ to $L^p$ for $p>1$ via the Riesz-Thorin interpolation theorem
