A Robust Framework for Modeling Preferences and its Applications in Revenue Management

在收益管理问题中，建立客户偏好模型是估计需求的一个基本挑战，因为不确定的需求主要取决于客户的替代行为。这样的建模尤其困难，因为偏好是潜在的和不可观察的。这个项目的广泛目标是开发一种易于处理的数据驱动的建模偏好方法，该方法对模型选择错误具有健壮性，并为相关决策问题开发有效的算法。本研究旨在发展偏好建模的基础理论，并有可能在实践中产生重大影响。为了促进这项工作的传播，以最大限度地扩大社会影响，国际和平研究所将侧重于：i)通过研究并将这项研究的结果纳入核心研究生课程对学生进行培训；ii)通过暑期REU项目增加本科生对研究的参与；iii)通过针对STEM教育的外联计划，包括妇女工程学会(SWE)和哈莱姆学校伙伴关系(HSP)，增加STEM教育的社会影响，特别注重增加未被充分代表的少数群体的参与；iv)与业界合作，将这项研究应用于实践。本项目的主要重点是研究建模偏好的马尔科夫框架。这个模型选择的框架很简单，但却非常强大，并且易于进行强大的概括，以捕获丰富的偏好模型类别。PI的目标是在这个项目中考虑两个大的方向：i)使用马尔可夫链转换的框架来模拟一类丰富的替代行为，以及ii)使用指数级大的偏好状态空间上的马尔可夫链来模拟一类分布在排列上的分布，例如更一般的Mlowes分布和最大熵分布。对这些模型的有效估计和优化算法将为采用易于处理的数据驱动方法进行选择建模奠定理论基础。随着当今世界大量数据的可用，这种方法可能会在许多应用程序中产生重大影响。

Modeling customer preferences is a fundamental challenge in estimating demand in revenue management problems since the uncertain demand crucially depends on the substitution behavior of the customers. Such modeling is especially difficult as the preferences are latent and unobservable. The broad goal of this project is to develop a tractable data-driven approach for modeling preferences that is robust to model selection errors, and develop efficient algorithms for related decision problems. This research aims at developing foundational theory for preference modeling that has potential of significant impact in practice. To facilitate the dissemination of this work to maximize societal impact, the PI will focus on: i) training of students through research and integration of the results from this research into core graduate curriculum, ii) increasing the involvement of undergraduate students in research through summer REU projects, iii) increasing the societal impact through outreach programs for local high-schools including Society for Women in Engineering (SWE) and Harlem School Partnership (HSP) for STEM Education with particular focus on increasing the participation of underrepresented minorities and iv) working with industry towards application of this research in practice.The main focus of this project is to study a Markovian framework for modeling preferences. This framework of modeling choice is simple yet very powerful and amenable to strong generalizations to capture a rich class of preference models. The PI aims to consider two broad directions in this project including: i) using the framework of Markov chain transitions to model a rich class of substitution behavior, and ii) using a Markov chain over an exponentially large state space of preferences to model a class of distribution over permutations such as Mallows and maximum entropy distributions more generally. Efficient estimation and optimization algorithms over these models would result in the theoretical foundations for a tractable data-driven approach to choice modeling. With the availability of large amount of data in today's world, such an approach has the potential of significant impact in many applications.