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

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

中文摘要:

      

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.