实验在 assortment 优化中的价值
The Value of Experiments in Assortment Optimization
Mohammadreza Ahmadnejadsaein, Amine Bennouna, Omar El Housni
AI 速览：研究在多项 logit 模型下，利用少量固定实验 assortment 的顾客选择数据，如何设计实验与最终 assortment 选择规则以最小化最坏情况遗憾。
Retailers can learn customer preferences by experimenting with different assortments. However, the cost of each experiment and the operational burden of repeatedly changing product offerings can make extensive experimentation impractical. We study how much a retailer can improve its final assortment decision using customer observations from one (or a very small number of) fixed experimental assortments. We consider the multinomial logit model, where product revenues are known but customer preferences are unknown. In this setting, we jointly design the experimental assortment and the rule for selecting a final assortment from observed customer choices to minimize worst-case regret: the expected revenue loss of the final assortment relative to an optimal assortment under the true preferences, maximized over possible customer preferences. We first characterize exactly the minimax regret and an optimal assortment when no experimentation is possible. We then show, surprisingly, that offering a single experimental assortment to just one customer can already substantially reduce regret, depending on how the products' revenues compare. We derive the exact minimax regret and an optimal experimental policy in this setting. When a single fixed experimental assortment is offered to many customers, we give a geometric characterization of the limiting minimax regret and construct an asymptotically optimal policy. Depending on product revenues, this single experiment can yield no improvement over no experimentation or nearly complete regret reduction. Finally, we extend our analysis to multiple experimental assortments chosen in advance, characterizing the limiting minimax regret, constructing asymptotically optimal policies, and identifying which collections of assortments allow worst-case regret to vanish as the number of customer observations grows.