Offline Data-Driven Decision Making with Applications to Assortment Optimization: Estimation and Inference

We present a unified offline decision making framework. In the first part, we consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred as Pessimistic ASsortment opTimizAtion (PASTA) following the spirit of pessimism. We show the algorithm identifies the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model and its generalizations, where the regret is shown to be minimax optimal. Joint work with Juncheng Dong, Weibin Mo, Zhengling Qi, Cong Shi, and Vahid Tarokh.

In the second part, we consider the inferential problem in assortment optimization. Uncertainty quantification for the optimal assortment is still largely unexplored despite its great practical significance. Instead of estimating and recovering the complete optimal offer set, decision-makers may only be interested in testing whether a given property holds true for the optimal assortment, such as whether they should include several products of interest in the optimal set, or how many categories of products the optimal set should include. We proposes a novel inferential framework for testing such properties. We reduce inferring a general optimal assortment property to quantifying the uncertainty associated with the sign change point detection of the marginal revenue gaps. We show the asymptotic normality of the marginal revenue gap estimator, and construct a maximum statistic via the gap estimators to detect the sign change point. Joint work with Shuting Shen, Alex Belloni, Xi Chen, and Junwei Lu.