Improved Confidence Regions and Optimal Algorithms for Online and Offline Linear MNL Bandits

In this work, we consider the data-driven assortment optimization problem under the linear multinomial logit(MNL) choice model. We first establish a improved confidence region for the maximum likelihood estimator (MLE) of the $d$-dimensional linear MNL likelihood function that removes the explicit dependency on a problem-dependent parameter $\kappa^{-1}$ in previous result (Oh and Iyengar, 2021), which scales exponentially with the radius of the parameter set. Building on the confidence region result, we investigate the data-driven assortment optimization problem in both offline and online settings.