Central Limit Theorems for Constructing Confidence Regions in Strictly Convex Multi-Objective Simulation Optimization

We consider the context of multi-objective simulation optimization (MOSO) with strictly convex objectives. We show that under certain types of scalarizations, a ( $1-\alpha$ ) -confidence region on the efficient set can be constructed if the scaled error field (over the scalarization parameter) associated with the estimated efficient set converges weakly to a mean-zero Gaussian process. The main result in this paper proves such a “Central Limit Theorem.” A corresponding result on the scaled error field of the image of the efficient set also holds, leading to an analogous confidence region on the Pareto set. The suggested confidence regions are still hypothetical in that they may be infinite-dimensional and therefore not computable, an issue under ongoing investigation.