论文标题
关于使用参数定义的估计器优化近似控制变体
On the Optimization of Approximate Control Variates with Parametrically Defined Estimators
论文作者
论文摘要
多模型的蒙特卡洛方法，例如多级蒙特卡洛（MLMC）和多重蒙特卡洛（MFMC），可以有效估计一组不同模型的多数利息的期望。最近，结果表明，MLMC和MFMC估计量都是近似控制变体（ACV）框架的实例[Gorodetsky等。 2020]。在同一项工作中，还表明，对于各种型号方案，手动尾的ACV估计器可以胜过MLMC和MFMC。由于没有理由相信这些手工量的估计器是无数可能的ACV估计器中最好的，因此在这项工作中采用了更通用的估计器构建方法。首先，制定了ACV估计器方差的一般形式。然后，该公式用于生成参数定义的估计器。这些参数定义的估计器允许在可能的ACV估计器的较大域进行优化。参数定义的估计器在大量模型方案上进行了测试，发现通过参数定义的估计器启用了更广泛的搜索域会导致更大的差异降低。
Multi-model Monte Carlo methods, such as multi-level Monte Carlo (MLMC) and multifidelity Monte Carlo (MFMC), allow for efficient estimation of the expectation of a quantity of interest given a set of models of varying fidelities. Recently, it was shown that the MLMC and MFMC estimators are both instances of the approximate control variates (ACV) framework [Gorodetsky et al. 2020]. In that same work, it was also shown that hand-tailored ACV estimators could outperform MLMC and MFMC for a variety of model scenarios. Because there is no reason to believe that these hand-tailored estimators are the best among a myriad of possible ACV estimators, a more general approach to estimator construction is pursued in this work. First, a general form of the ACV estimator variance is formulated. Then, the formulation is utilized to generate parametrically-defined estimators. These parametrically-defined estimators allow for an optimization to be pursued over a larger domain of possible ACV estimators. The parametrically-defined estimators are tested on a large set of model scenarios, and it is found that the broader search domain enabled by parametrically-defined estimators leads to greater variance reduction.
