Multinomial Logit Contextual Bandits: Provable Optimality and Practicality

We consider a sequential assortment selection problem where the user choice is given by multinomial logit (MNL) model whose parameters are unknown. In each period, learning agent observes d-dimensional contextual information about and N available items, offers an of size K to user, bandit feedback item chosen from assortment. propose upper confidence bound based algorithms for this MNL bandit. The first algorithm simple practical method that achieves O(d√T) regret over T rounds. Next, we second which O(√dT) regret. This matches lower problem, up logarithmic terms, improves on best-known result √d factor. To establish sharper bound, present non-asymptotic maximum likelihood estimator may be independent interest as its own theoretical contribution. then revisit simpler, significantly more practical, show variant optimal broad class important applications.