On Pareto Optimality for the Multinomial Logistic Bandit

• URL: http://arxiv.org/abs/2501.19277v1
• Date: Fri, 31 Jan 2025 16:42:29 GMT
• Title: On Pareto Optimality for the Multinomial Logistic Bandit
• Authors: Jierui Zuo, Hanzhang Qin,
• Abstract summary: We provide a new online learning algorithm for tackling the Multinomial Logit Bandit problem. Despite the challenges posed by the MNL model, we develop a novel Upper Confidence Bound (UCB)-based method. We develop theoretical guarantees characterizing the tradeoff between regret and estimation error for the MNL-Bandit problem.
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• Abstract: 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.

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