Stochastic Optimization with Model Uncertainty and Learning

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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.