A1685
Title: Online inference for optimal assortments via minimal directional perturbation radius of a max-difference statistic
Authors: Shuting Shen - National University of Singapore (Singapore) [presenting]
Abstract: An inferential procedure is developed for testing structural properties of the revenue-maximizing assortment under a high-dimensional contextual multinomial logit model with sequentially adaptive data collection. The problem is challenging because the map from utility parameters to the optimal assortment is non-smooth and combinatorial, while the adaptive design induces complex temporal dependence. The procedure is based on data collected under a dynamic policy that updates assortments using $\ell_1$-penalized online estimation for contextual variable selection, and then performs post-learning inference on whether the optimal assortment satisfies a deployable structural rule, such as a category-mix requirement, or feasibility under inventory or resource constraints. The method is built on a revenue max-difference statistic with local perturbations of the revenue estimates, capturing uncertainty in both direction and magnitude: random unit directions account for directional error, and the minimal perturbation radius quantifies magnitude uncertainty. New tools based on martingale coupling and anti-concentration for differences of Gaussian maxima are developed. The resulting procedure is substantially more powerful than uniform error bound approaches. Finite-sample estimation rates, exact support recovery, and a non-asymptotic error decomposition for the debiased estimator are established, and asymptotic size control and power consistency are proven.
