An Optimization Framework for Dynamic A-B Testing

a - b测试是一种用于比较两种设计方案有效性的统计方法。它广泛用于临床试验和电子商务，以比较医疗计划或营销和零售策略的性能。这个项目的重点是通过利用动态优化理论的最新进展，为有效的a - b测试方案创建一个框架。虽然该项目将考虑广义模型，但一个特别的重点将放在适应性临床试验上，目的是确定一种新药或治疗方法是否能改善现有的治疗方法。在这些动态医学试验中，考虑到早期参与者的信息，对每个患者分配哪种治疗的决定是实时做出的。该奖项将支持研究生的研究，该项目的研究成果将被整合到新的分析学硕士项目的课程中。PI将开发一种基于动态优化的最佳a - b测试设计的新方法。该项目旨在建立这种试验设计中隐含的动态优化问题受益于“状态空间崩溃”。这将有助于解决目前在计算上难以解决的大规模问题。从理论的角度来看，这将需要解决随机向量着色问题，这本身就是一个基本问题。从实践角度来看，该项目将有助于在面对高维受试者协变量时设计最优试验；当治疗效果在可观察的协变量中高度非线性时，产生优化效率的能力；最后，让试验设计者有能力在选择偏差（或公平性）与统计效率之间进行最佳权衡。与业界合作伙伴的合作将被用来提高这个研究项目的实际影响，并丰富学生的课堂体验。

A-B testing is a statistical method used to compare the effectiveness of two design options. It is widely used in clinical trials and e-commerce to compare the performance of medical treatment plans or marketing and retail strategies. This project focuses on creating a framework for efficient A-B testing schemes by leveraging recent advances in the theory of dynamic optimization. While the project will consider generalized models, a particular focus will be on adaptive clinical trials that aim to determine whether a new drug or treatment improves on an existing treatment. In these dynamic medical trials, the decision of which treatment to assign to each patient is made in real time, taking into consideration information from the earlier participants. The award will support graduate student research, and findings resulting from this project will be integrated into coursework for a new Masters in Analytics program.The PI will develop a new approach to the design of optimal A-B tests, rooted in dynamic optimization. The project aims to establish that the dynamic optimization problem implicit in the design of such a test benefits from a "state space collapse". This would facilitate the solution of large-scale problems that are currently computationally intractable. From a theoretical perspective, this will entail the solution of a random vector-coloring problem that is fundamental in its own right. From a practical perspective, the project will facilitate the design of optimal trials in the face of high-dimensional subject covariates; yield the ability to optimize for efficiency when treatment effects are highly non-linear in observable covariates; and finally, give trial designers the ability to optimally trade off selection bias (or fairness) against statistical efficiency. Collaboration with industry partners will be used to enhance the practical impact of this research project, and to enrich the classroom experience for students.