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.

翻译：我们提出了一种新的在线学习算法，用于解决多项逻辑斯蒂克老虎机问题。尽管MNL模型的组合性质带来了挑战，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，实现了近似帕累托最优性。我们通过信息论界建立了理论保证，刻画了MNL老虎机问题中遗憾与估计误差之间的权衡关系，并提出了一种改进的UCB算法，该算法引入强制探索机制以提高参数估计精度，同时保持较低的遗憾值。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。