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Optimization via simulation (OvS) procedures that assume the simulationinputs are generated from the real-world distributions are subject to the riskof selecting a suboptimal solution when the distributions are substituted withinput models estimated from finite real-world data -- known as input modelrisk. Focusing on discrete OvS, this paper proposes a new Bayesian frameworkfor analyzing input model risk of implementing an arbitrary solution, $x$,where uncertainty about the input models is captured by a posteriordistribution. We define the $\alpha$-level risk set of solution $x$ as the setof solutions whose expected performance is better than $x$ by a practicallymeaningful margin $(>\delta)$ given common input models with significantprobability ($>\alpha$) under the posterior distribution. The user-specifiedparameters, $\delta$ and $\alpha$, control robustness of the procedure to thedesired level as well as guards against unnecessary conservatism. An empty riskset implies that there is no practically better solution than $x$ withsignificant probability even though the real-world input distributions areunknown. For efficient estimation of the risk set, the conditional meanperformance of a solution given a set of input distributions is modeled as aGaussian process (GP) that takes the solution-distributions pair as an input.In particular, our GP model allows both parametric and nonparametric inputmodels. We propose the sequential risk set inference procedure that estimatesthe risk set and selects the next solution-distributions pair to simulate usingthe posterior GP at each iteration. We show that simulating the pair expectedto change the risk set estimate the most in the next iteration is theasymptotic one-step optimal sampling rule that minimizes the number ofincorrectly classified solutions, if the procedure runs without stopping.

Sequential Bayesian Risk Set Inference for Robust Discrete Optimization via Simulation