Stochastic Optimization with Model Uncertainty and Learning

运筹学和管理科学中不确定性决策的理论基础依赖于一个完全确定的概率模型的发展。在一些统计假设下，制定了一个概率模型。最优决策，然后从这个模型。在实际实施最优决策时，利用数据估计参数来校正概率模型，然后实施概率模型所期望的最优决策。这种方法完全忽略了概率模型的误差和参数估计误差对最优决策的影响。这些错误可能会使模型在实践中无效，导致理论与实践之间的差距。这笔赠款提供资金，用于开发建模方法，解释这些错误，并为解决方案的方法，以确定最佳决策时，有这样的建模错误的发展。具体而言，将开发一种系统的建模方法，其中将开发一系列具有学习功能的模型。这个集合将包含一个概率模型，尽管是明确未知的，但它精确地表示了真实的系统。解决方案的方法将找到一个最佳的决策，使不知道确切的概率模型的影响最小化。因此，在实践中，这种方法所规定的决策的实施建模误差的影响是最小的。如果成功的话，本研究的结果将减少理论和实践之间的差距在运筹学和管理科学。一个系统的建模方法，将在实践中更可靠的研究将出现。它将具有学习能力，随着时间的推移，使模型规定的决策越来越好。该解决方案的方法将找到一个最佳的决策，使得在实践中由该方法规定的决策的实现中的建模误差的影响是最小的。新的决策实践者和教授将接受这种新方法的培训。

Theoretical foundation of operations research and management science for decision making under uncertainty rely on the development of a fully specified probability model. A probability model is formulated under some statistical assumptions. Optimal decision is then derived from this model. When implementing the optimal decision in practice, data is used to estimate the parameters to calibrate the probability model and the optimal decision purported by the probability model is then implemented. This approach totally ignores the effects of errors in the formulation of the probability model and the errors in the estimation of the parameters on the optimal decision. These errors can make the model ineffective in practice leading to a gap between theory and practice. This grant provides funding for developing modeling methodologies that accounts for these errors and for the development of solution approaches for identifying the optimal decisions when there are such modeling errors. Specifically, a systematic modeling methodology where a collection of models with learning will be developed. This collection will contain a probability model, though explicitly unknown, that accurately represents the real system. The solution approach will find an optimal decision such that the effect of not knowing the exact probability model is minimized. Hence the impact of modeling errors in the implementation of the decision prescribed by this approach in practice is minimal.If successful, the results of this research will reduce that gap between theory and practice in operations research and management science. A systematic modeling methodology that will be more reliable in practice will emerge out of this research. It will have the learning capability to make the decision prescribed by the model better and better over time. The solution approach will find an optimal decision such that the impact of modeling errors in the implementation of the decision prescribed by this approach in practice is minimal. New decision making practitioners and professors will be trained in this new approach.