A Multilevel Simulation Optimization Approach for Quantile Functions
提出一种基于多层元模型（协同克里金）的算法，通过利用低分位数更易优化且更准确的特点，逐步逼近目标分位数，从而高效优化仿真中的分位数函数，适用于需要评估风险与变异的决策场景。
A quantile is a popular performance measure for a stochastic system to evaluate its variability and risk. To reduce the risk, selecting the actions that minimize the tail quantiles of some loss distributions is typically of interest for decision makers. When the loss distribution is observed via simulations, evaluating and optimizing its quantile can be challenging, especially when the simulations are expensive as it may cost a large number of simulation runs to obtain accurate quantile estimators. In this work, we propose a multilevel metamodel (cokriging)-based algorithm to optimize quantiles more efficiently. Utilizing nondecreasing properties of quantiles, we first search on cheaper and informative lower quantiles, which are more accurate and easier to optimize. The quantile level iteratively increases to the objective level, and the search has a focus on the possible promising regions identified by the previous levels. This enables us to leverage the accurate information from the lower quantiles to find the optimums faster and improve algorithm efficiency.