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 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.

翻译：本文针对多项Logit老虎机问题提出了一种新的在线学习算法。尽管MNL模型具有组合复杂性带来的挑战，我们开发了一种基于置信上界的新型方法，通过平衡遗憾最小化与商品组合收益及MNL参数估计误差，实现了帕累托最优。我们通过信息论界建立了MNL老虎机问题中遗憾与估计误差权衡的理论保证，并提出一种改进的UCB算法，该算法通过强制探索机制在保持低遗憾的同时提升参数估计精度。我们的分析为动态商品组合优化中如何最优平衡收益获取与参数估计提供了关键见解。