On (Approximate) Pareto Optimality for the Multinomial Logistic Bandit
This work addresses dynamic assortment optimization for online platforms, providing an incremental improvement in balancing revenue and parameter estimation.
The paper tackles the Multinomial Logit Bandit problem by developing a novel UCB-based algorithm that achieves approximate Pareto optimality, balancing regret minimization and estimation error with theoretical guarantees.
We provide a new online learning algorithm for tackling the Multinomial Logit Bandit (MNL-Bandit) problem. Despite the challenges posed by the combinatorial nature of the MNL model, we develop a novel Upper Confidence Bound (UCB)-based method that achieves Approximate Pareto Optimality by balancing regret minimization and estimation error of the assortment revenues and the MNL parameters. We develop theoretical guarantees characterizing the tradeoff between regret and estimation error for the MNL-Bandit problem through information-theoretic bounds, and propose a modified UCB algorithm that incorporates forced exploration to improve parameter estimation accuracy while maintaining low regret. Our analysis sheds critical insights into how to optimally balance the collected revenues and the treatment estimation in dynamic assortment optimization.