Our paper studies how to determine the personalized incentive for each customer to learn her true preference in the assortment optimization and product design problem. We provide algorithms that sequentially decide the personalized incentives based on the evaluated customer's contribution to the revenue increase. We show that compared to the naive supervised learning algorithm that provides fixed incentives, our algorithm can reduce the total cost significantly while achieving high revenue.

We introduce the concept of randomization into the robust assortment optimization liter-ature. We show that the firm can improve its worst-case expected revenues by selecting an assortment randomly according to a prudently designed probability distribution. We demonstrate this potential benefit of randomization both theoretically in an abstract problem formulation and empirically across three choice models: the multinomial logit model, the Markov chain model, and the preference ranking model.

We study dynamic joint assortment and pricing over a finite time period. The goal is to maximize the expected cumulative revenue. We propose a new doubly high-dimensional contextual bandit model to formulate the problem. We developed a computationally tractable algorithm and provide a convergence rate for it. The numerical results of applying our method to a real-world online retail data set demonstrate the efficiency of our method, which is further supported by extensive simulations.