Stochastic Optimization with Model Uncertainty and Learning

具有模型不确定性和学习的随机优化

• 批准号: 0500503
• 负责人: Andrew Lim
• 金额: $ 38.99万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0500503&HistoricalAwards=false
• 关键词: Stochastic; Optimization; Model; Uncertainty; Learning

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.

运筹学和管理科学在不确定条件下进行决策的理论基础有赖于完全特定的概率模型的发展。在一定的统计假设下，建立了概率模型。然后由该模型得出最优决策。在实际实施最优决策时，利用数据估计参数，对概率模型进行标定，从而实现概率模型所声称的最优决策。该方法完全忽略了概率模型的建立误差和参数估计误差对最优决策的影响。这些错误可能会使该模型在实践中无效，导致理论与实践之间的差距。这笔赠款提供资金，用于开发解释这些错误的建模方法，以及开发解决方案，以便在出现此类建模错误时确定最佳决策。具体地说，是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，尽管它是明确未知的，但它准确地表示了真实的系统。求解方法将找到一个最优决策，从而使不知道确切概率模型的影响最小化。因此，模型误差对实践中该方法所规定的决策实施的影响是最小的。如果成功，本研究的结果将缩小运筹学和管理科学中理论与实践之间的差距。这项研究将产生一种在实践中更加可靠的系统建模方法。随着时间的推移，它将具有学习能力，使模型规定的决策越来越好。该解决方法将找到一个最优决策，以便在实施该方法所规定的决策时，建模误差的影响在实践中最小。新的决策实践者和教授将接受这种新方法的培训。