基于自适应多重重要性抽样的样本均值逼近最优值的中偏差

Moderate Deviations for the Optimal Values of Sample Average Approximation with Adaptive Multiple Importance Sampling

中文关键词:  自适应多重重要性抽样  鞅差  中偏差

英文关键词:adaptive multiple importance sampling  martingale difference  moderate deviation

中文摘要:

      本文采用自适应多重重要性抽样的样本均值逼近方法来探讨最优值的中偏差.利用鞅差的中偏差原理和适当的Delta方法,我们建立了一个最优值的中偏差原理.此外,对于随机规划的泛函形式,我们得到了其最优值的一个泛函型中偏差原理.

英文摘要:

      In this paper, we use sample average approximation with adaptive multiple importance sampling to explore moderate deviations for the optimal values. Utilizing the moderate deviation principle for martingale differences and an appropriate Delta method, we establish a moderate deviation principle for the optimal value. Moreover, for a functional form of stochastic programming, we obtain a functional moderate deviation principle for its optimal value.