2015/12/28 by Qi Sun, Sun, Qi, Ming Ju +1
Decision Sciences · Mathematics · #FOS: Mathematics #Forecasting Techniques and Applications #Mathematical Approximation and Integration #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.1512.08403
openalex publication_date 2015/12/28 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
In this paper, we consider the implementation of multi-level Monte Carlo\nmethod to a stochastic optimal control problem with log-normal coefficients and\nits surrogate model problem. From the perspective of two optimization problems,\ni.e., minimizing the accuracy using a fixed computational cost and minimizing\nthe total computational cost to attain a given accuracy, we derive formulas to\ndetermine the optimal sample sizes for each level of multi-level Monte Carlo\nmethod. Furthermore, we put forward the multi-level Monte Carlo algorithm for\nour stochastic optimal control problem and some tricks to deal with the\nmulti-level log-normal coefficients. Finally, we present the numerical results\nof both the elliptic SPDEs and our control problem to validate the\neffectiveness over the traditional Monte Carlo method.\n