Value of One Data Point: Active Label Acquisition in Assortment Optimization

Abstract

Predicting customers' preferences based on their features is crucial for personalized assortment optimization. When building this prediction model, using informative data can significantly increase the expected revenue from personalized assortments. This paper studies how to sequentially collect informative data to construct this prediction model. We introduce a novel concept, the 'value of one data point,' which evaluates the marginal contribution of acquiring a specific customer's preference to the expected revenue in personalized assortment optimization, given the existing training set. Notably, this value drops to zero once the optimal assortment for this specific customer is determined. To estimate this value and identify important customers for acquiring their preferences, we derive a feature-dependent upper bound. This bound provides significant insights into the importance of each data point for revenue growth. Based on this upper bound, we develop a personalized incentive policy for effectively collecting survey data from customers to obtain their preferences. We provide non-asymptotic guarantees for both the cumulative incentives and the revenue from the final prediction model. Theoretically, we show that our personalized incentive policy requires smaller cumulative incentives than any fixed incentive policy to achieve the same level of revenue. Additionally, our numerical experiments with real-world and synthetic datasets validate the effectiveness of our personalized incentive algorithms over fixed strategies.

Keywords: active label acquisition, personalized incentive, assortment optimization, product selection