Stochastic Matching Bandits under Preference Feedback

Jung-hun Kim, Min-hwan Oh

Keywords: Matching bandits, Preference Feedback

TL;DR: In this study, we propose a new bandit framework of stochastic matching employing the Multinomial Logit (MNL) choice model with feature information.

Abstract:

In this study, we propose a new bandit framework of stochastic matching employing the Multinomial Logit (MNL) choice model with feature information. In this framework, agents on one side are assigned to arms on the other side, and each arm stochastically accepts an agent among the assigned pool of agents based on its unknown preference, allowing a possible outside option of not accepting any.
The objective is to minimize regret by maximizing the probability of successful matching.
For this framework, we first propose an elimination-based algorithm that achieves a regret bound of $\tilde{O}\big(K\sqrt{rKT} \big)$ over time horizon $T$, where $K$ is the number of arms and $r$ is the rank of feature space. Furthermore, we propose an approach to resolve the computation issue regarding combinatorial optimization in the algorithm.
Lastly, we evaluate the performances of our algorithm through experiments comparing with the existing showing the superior performances of our algorithm.

Primary Area: learning theory

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Submission Number: 2717