Thompson Sampling for the MNL-Bandit
Shipra Agrawal, Vashist Avadhanula, Vineet Goyal, Assaf Zeevi

TL;DR
This paper introduces a Thompson Sampling approach for the MNL-Bandit problem, a sequential subset selection task with unknown parameters, achieving near-optimal regret and strong numerical results.
Contribution
It adapts Thompson Sampling to the MNL-Bandit problem, providing a near-optimal regret guarantee and demonstrating effective numerical performance.
Findings
Achieves near-optimal regret bounds.
Demonstrates strong numerical performance.
Addresses a broad class of exploration-exploitation problems.
Abstract
We consider a sequential subset selection problem under parameter uncertainty, where at each time step, the decision maker selects a subset of cardinality from possible items (arms), and observes a (bandit) feedback in the form of the index of one of the items in said subset, or none. Each item in the index set is ascribed a certain value (reward), and the feedback is governed by a Multinomial Logit (MNL) choice model whose parameters are a priori unknown. The objective of the decision maker is to maximize the expected cumulative rewards over a finite horizon , or alternatively, minimize the regret relative to an oracle that knows the MNL parameters. We refer to this as the MNL-Bandit problem. This problem is representative of a larger family of exploration-exploitation problems that involve a combinatorial objective, and arise in several important application domains. We…
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Auction Theory and Applications · Optimization and Search Problems
