Distributionally robust optimization and its applications

决策往往需要在一个人对他正在处理的问题的某些参数不完全了解的情况下做出。例如，在资产组合选择问题中，资产的未来价值是不确定的，或者在库存管理问题中，产品的未来市场需求可能会发生变化。分布鲁棒优化是随机规划的一种推广，可以为管理此类决策问题提供必要的指导，因为它可以解释分布模型选择中的模糊性。这种模糊性在实践中经常出现，并且可能使随机规划的解决方案具有误导性。我的研究计划的使命有两个方面。1)我计划发展理论，这将有助于回答重要的开放性问题，这些问题阻碍了分布鲁棒模型的大规模应用。 2)我还计划在将方法论与重要的工业问题相结合方面发挥主导作用。这些措施包括： - 资源分配问题，如长期退休计划投资组合的选择和估值。 - 库存管理问题，例如航空公司在了解实际航班需求之前组成机队时所面临的问题。 - 由于对可用资源知之甚少，不确定性无处不在，开发矿山和生产可再生能源。 - 营销问题，如如何提出更有可能被在线客户购买的项目或向他展示最有效的广告。 我希望分布鲁棒优化及其衍生物很快成为不确定性决策领域的常见实践。

Decisions often need to be made in situations where one has incomplete knowledge about some of the parameters of the problem that he is addressing. This is for example the case in a problem of portfolio selection where the future value of an asset is uncertain, or in an inventory management problem where the future market demand for a product might be subject to changing. Distributionally robust optimization is a generalization of stochastic programming that can provide essential guidance in managing such decision problems since it can account for ambiguity in the choice of a distribution model. Such ambiguity is often present in practice and can make the solution of a stochastic program misleading. The mission of my research program is two-fold. 1) I plan to develop theory that will help answer important open questions that are preventing the distributionally robust model to be applicable at a large scale. 2) I also plan to take a leading role in the integration of the methodology to important industrial problems. These will include: - Resource allocation problems such as the selection and valuation of a portfolio of investment for long term retirement plans. - Inventory management problems such as the problem faced by airline companies when composing a fleet of aircraft prior to knowing the actual demand for flights. - Development of mines and production of renewable energy where uncertainty is omnipresent due to the little knowledge of the available resources. - Marketing problems such as how to propose items more likely to be purchased by an online customer or present him the most effective ad. My hope is that distributionally robust optimization and its derivatives soon become common practice in the field of decision making under uncertainty.