Abstract: Motivated by real-world applications such as fast fashion retailing and online advertising, the Multinomial Logit Bandit (MNL-bandit) is a popular model in online learning and operations research, and has attracted much attention in the past decade. In this paper, we give efficient algorithms for {\em pure exploration} in MNL-bandit. Our algorithms achieve {\em instance-sensitive} pull complexities. We also complement the upper bounds by an almost matching lower bound.