We consider a decision maker who must choose an action in order to maximize a reward function that depends also on an unknown parameter Θ. The decision maker can delay taking the action in order to experiment and gather additional information on Θ. We model the decision maker's problem using a Bayesian sequential experimentation framework and use dynamic programming and diffusion-asymptotic analysis to solve it. For that, we scale our problem in a way that both the average number of experiments that is conducted per unit of time is large and the informativeness of each individual experiment is low. Under such regime, we derive a diffusion approximation for the sequential experimentation problem, which provides a number of important insights about the nature of the problem and its solution. Our solution method also shows that the complexity of the problem grows only quadratically with the cardinality of the set of actions from which the decision maker can choose. We illustrate our methodology and results using a concrete application in the context of assortment selection and new product introduction. Specifically, we study the problem of a seller who wants to select an optimal assortment of products to launch into the marketplace and is uncertain about consumers' preferences. Motivated by emerging practices in e-commerce, we assume that the seller is able to use a crowdvoting system to learn these preferences before a final assortment decision is made. In this context, we undertake an extensive numerical analysis to assess the value of learning and demonstrate the effectiveness and robustness of the heuristics derived from the diffusion approximation.
Robust Sequential Experimental Design for A/B Testing
Yunnan Key Laboratory of Statistical Modeling and Data Analysis（云南统计建模与数据分析重点实验室）；Yunnan University（云南大学）；School of Mathematical Sciences（数学科学学院）；Zhejiang University（浙江大学）；Department of Statistics（统计系）；London School of Economics and Political Science（伦敦政治经济学院）；School of Statistics and Data Science（统计与数据科学学院）；Shanghai University of Finance and Economics（上海财经大学）；East China Normal University（华东师范大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Private Sequential Hypothesis Testing for Statisticians: Privacy, Error Rates, and Sample Size
Harvard John A. Paulson School Of Engineering And Applied Sciences（哈佛大学约翰·A·保尔森工程与应用科学学院）；Georgia Institute of Technology（佐治亚理工学院）；H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（佐治亚理工学院H·米尔顿·斯图尔特工业与系统工程学院）；Department of Industrial Engineering and Operations Research, Columbia University（哥伦比亚大学工业工程与运筹学系）
Sequential Kernel-based Conditional Independence Testing via Adaptive Betting
Department of Computer Science, University of British Columbia, Vancouver, Canada（不列颠哥伦比亚大学计算机科学系，温哥华，加拿大）；Alberta Machine Intelligence Institute, Edmonton, Canada（阿尔伯塔机器智能研究所，爱德蒙顿，加拿大）
Global Sequential Testing for Multi-Stream Auditing
Mathematical Institute for Data Science (MINDS), Johns Hopkins University（数据科学数学研究所（MINDS），约翰霍普金斯大学）；Department of Biomedical Engineering, Johns Hopkins University（生物医学工程系，约翰霍普金斯大学）；Amazon Responsible AI（亚马逊负责任人工智能）
Asymptotically Optimal Sequential Testing with Markovian Data
Indian Institute of Science, Bangalore（班加罗尔印度科学学院）；Indian Institute of Technology, Hyderabad（海得拉巴印度理工学院）；Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189 – CRIStAL（里尔大学、法国国家科学研究中心、中央里尔学院、UMR 9189 – CRIStAL）
Sequential Permutation Testing of Random Forest Variable Importance Measures
Institute of General Practice and Health Services Research（全科医学与卫生服务研究所）；Institute of AI and Informatics in Medicine（医学人工智能与信息学研究所）；Technical University of Munich（慕尼黑工业大学）；Institute for Medical Information Processing, Biometry and Epidemiology（医学信息处理、生物统计学与流行病学研究所）；University of Munich（慕尼黑大学）
Cost-optimal Sequential Testing via Doubly Robust Q-learning
Department of Statistics and Data Science, National University of Singapore（国立新加坡大学统计与数据科学系）；Public Health Sciences Division, Fred Hutch（Fred Hutch公共卫生科学系）；Department of Biomedical Data Science, Stanford University School of Medicine（斯坦福大学医学院生物医学数据科学系）；Department of Biostatistics, Harvard T.H. Chan School of Public Health（哈佛大学T.H. Chan公共卫生学院生物统计学系）
