A Multilevel Simulation Optimization Approach for Quantile Functions

A quantile is a popular performance measure for stochastic system to evaluate its variability and risk. To reduce the risk, selecting actions that minimize tail quantiles of some loss distributions typically interest decision makers. When distribution observed via simulations, evaluating optimizing can be challenging, especially when simulations are expensive as it may cost large number simulation runs obtain accurate estimators. In this work, we propose multilevel metamodel (cokriging)-based algorithm optimize more efficiently. Utilizing nondecreasing properties quantiles, first search on cheaper informative lower which easier optimize. The level iteratively increases objective level, has focus possible promising regions identified by previous levels. This enables us leverage information from find optimums faster improve efficiency.