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We consider a simulation-based ranking and selection (R&S) problem with input uncertainty, in which unknown input distributions can be estimated using input data arriving in batches of varying sizes over time. Each time a batch arrives, additional simulations can be run using updated input distribution estimates. The goal is to confidently identify the best design after collecting as few batches as possible. We first introduce a moving average estimator for aggregating simulation outputs generated under heterogenous input distributions. Then, based on a sequential elimination framework, we devise two major R&S procedures by establishing exact and asymptotic confidence bands for the estimator. We also extend our procedures to the indifference zone setting, which helps save simulation effort for practical usage. Numerical results show the effectiveness and necessity of our procedures in controlling error from input uncertainty. Moreover, the efficiency can be further boosted through optimizing the “drop rate” parameter, which is the proportion of past simulation outputs to discard, of the moving average estimator. 

The performance of a model predictive controller depends on the accuracy of the objective and prediction model of the system. Although significant efforts have been dedicated to improving the robustness of model predictive control (MPC), they typically do not take a risk-averse perspective. In this paper, we propose a risk-aware MPC framework, which estimates the underlying parameter distribution using online Bayesian learning and derives a risk-aware control policy by reformulating classical MPC problems as Bayesian Risk Optimization (BRO) problems. The consistency of the Bayesian estimator and the convergence of the control policy are rigorously proved. Furthermore, we investigate the consistency requirement and propose a risk monitoring mechanism to guarantee the satisfaction of the consistency requirement. Simulation results demonstrate the effectiveness of the proposed approach.