A0617
Title: Rate-optimal online learning for dynamic assortment selection with positioning
Authors: Yiyun Luo - School of Statistics and Management, Shanghai University of Finance and Economics (China) [presenting]
Abstract: In online retailing, the seller aims to offer an assortment of items with maximized expected revenue. A new online learning problem is introduced called dynamic assortment selection with positioning (DAP), which additionally investigates the positioning of items within the assortment. Specifically, customers make purchases based on the item's attractiveness as the product of the position effect and unknown preference parameter through a multinomial logit choice model. The objective is to maximize the revenue over a finite horizon. It is first demonstrated that any assortment-only algorithm that neglects position effects results in linear regrets. To address this gap, the truncated linear regression upper confidence bound (TLR-UCB) policy is proposed. TLR-UCB utilizes a novel geometric linear-bandit-type feedback structure to construct upper confidence bounds (UCB) for unknown preference parameters, accounting for both random and adaptive position effects. To ensure the validity of UCB construction, TLR-UCB adopts a truncation technique for conditional geometric responses before applying linear regression. In theory, a regret upper bound of $O(T^(1/2))$ is established for TLR-UCB, matching the derived regret lower bound for the DAP problem. Extensive experiments demonstrate the superior performance of TLR-UCB by incorporating the position effects into the dynamic assortment selection process.
