用核积分嵌套法加速复杂期望值估计，样本更少效果更好。
Nested Expectations with Kernel Quadrature
- 采用嵌套核积分构造新估计器，利用函数光滑性提升精度
- 理论证明收敛速度优于传统蒙特卡洛与多层蒙特卡洛方法
- 在贝叶斯优化、期权定价等实际任务中显著减少所需样本量
本文研究嵌套期望估计这一复杂计算任务。现有方法如嵌套蒙特卡洛或多层蒙特卡洛虽具一致性，但需在内外层均消耗大量样本才能收敛。本文提出一种新型估计器，由嵌套核积分构成，并证明当被积函数足够光滑时，其收敛速度优于所有基线方法。实验表明，在贝叶斯优化、期权定价及健康经济学等真实应用场景中，该方法确实能以更少样本实现准确估计。
原文摘要 · Abstract (English)
This paper considers the challenging computational task of estimating nested expectations. Existing algorithms, such as nested Monte Carlo or multilevel Monte Carlo, are known to be consistent but require a large number of samples at both inner and outer levels to converge. Instead, we propose a novel estimator consisting of nested kernel quadrature estimators and we prove that it has a faster convergence rate than all baseline methods when the integrands have sufficient smoothness. We then demonstrate empirically that our proposed method does indeed require fewer samples to estimate nested expectations on real-world applications including Bayesian optimisation, option pricing, and health economics.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。