A0611
Title: Optimal assortment inference within an online learning framework
Authors: Shuting Shen - National University of Singapore (Singapore) [presenting]
Abstract: The modern retailing system is witnessing fast updating in customer behaviors, entailing adaptive policies to capture the dynamics of customer preferences. To manage the risks associated with changing customer preferences, it is important to develop an online framework that quantifies the uncertainty of the optimal assortment adaptively. The combinatorial inference of the optimal assortment is studied under the contextual multinomial logit model. Customer choice outcomes are actively collected over a series of time points, where the contextual information includes embedding vectors that capture the customer-product dynamics and revenue parameters. The offer set is adaptively selected at each time based on historical data. An inferential procedure is proposed that constructs a discrete confidence set for the true optimal assortment, facilitating inference on key properties of the optimal assortment. The temporal dependency and combinatorial structure of the Hessian matrix create challenges for convergence analysis. To address these, new anti-concentration bounds are developed for the Gaussian maxima difference. Furthermore, the high dimensionality is addressed by employing discretization and subspace projection techniques. Theoretical guarantees are provided on both the validity and power of the inferential procedure, and information-theoretic lower bounds are established for the required signal strength, which match the upper bounds of the procedure up to logarithmic factors.
