讲座时间：9月2日9:30-11:30

讲座地点：管楼G416

讲座主题：Optimal Assortment Inference within an Online Learning Framework

讲座嘉宾简介

Shen Shuting is an Assistant Professor of Statistics and Data Science at the National University of Singapore. Before joining NUS, she was a postdoctoral fellow at the Fuqua School of Business and the Department of Biostatistics & Bioinformatics at Duke University, jointly supervised by Dr. Alexandre Belloni and Dr. Ethan X. Fang. She obtained her PhD in Biostatistics from Harvard University, where she was jointly supervised by Dr. Xihong Lin and Dr. Junwei Lu. Her research interests primarily include large-scale inference, combinatorial inference, choice model asymptotics, operations research theory, applied probability, and distributed computing.

讲座摘要

The modern retailing system is witnessing fast updating in product features and customer behaviors, entailing adaptive policies that can effectively capture the dynamics of customer preferences. To optimize potential revenues and manage the risks associated with changing customer preferences, it is important to develop an online framework that quantifies the uncertainty of the optimal assortment adaptively.

We study the combinatorial inference of the optimal assortment within the framework of the contextual multinomial logit model. In this setting, customer choice outcomes are actively collected over a series of T time points, where the contextual information for n products, including embedding vectors that capture the customer-product dynamics and evolving market trends, as well as revenue parameters, varies over time. Using a dynamic policy, the offer set is adaptively selected at each time point based on historical data. We propose an inferential procedure that constructs a discrete confidence set for the true optimal assortment at the end of the time series, facilitating inference on key properties of the optimal assortment, such as the number of product categories to include in the offer set.

The temporal dependency and combinatorial structure of the Hessian matrix of the log-likelihood function create challenges for convergence analysis. To address these, we develop new probabilistic results on anti-concentration bounds for the difference between the maxima of two Gaussian random vectors. Furthermore, we address the high dimensionality of the combinatorial inference problem by employing discretization via e--covering and subspace projection techniques. We provide theoretical guarantees on both the validity and power of our inferential procedure, and establish information-theoretic lower bounds for the required signal strength, which match the upper bounds of our procedure up to logarithmic factors.