Instance-Sensitive Algorithms for Pure Exploration in Multinomial Logit Bandit

TL;DR

This paper introduces efficient, instance-sensitive algorithms for pure exploration in the Multinomial Logit Bandit model, addressing a gap in bandit theory with theoretical bounds and practical implications.

Contribution

It provides the first efficient algorithms for pure exploration in MNL-bandits with instance-sensitive complexity guarantees and matching lower bounds.

Findings

Algorithms achieve instance-sensitive pull complexities.

Upper bounds are complemented by nearly matching lower bounds.

Advances understanding of pure exploration in MNL-bandit models.

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. However, it is a bit surprising that pure exploration, a basic problem in bandit theory, has not been well studied in MNL-bandit so far. In this paper we give efficient algorithms for pure exploration in MNL-bandit. Our algorithms achieve instance-sensitive pull complexities. We also complement the upper bounds by an almost matching lower bound.