Event
Weekly OptiML Lab Group Meeting
Short summary
In this seminar, I will talk about my own paper “Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion” (Lee et al., AISTATS 2024).
Abstract
(taken directly from the paper)
Logistic bandit is a ubiquitous framework of modeling usersβ choices, e.g., click vs. no click for advertisement recommender system. We observe that the prior works overlook or neglect dependencies in πβ₯βπββ2, where πβββπ is the unknown parameter vector, which is particularly problematic when π is large, e.g., πβ₯π. In this work, we improve the dependency on π via a novel approach called {\it regret-to-confidence set conversion (R2CS)}, which allows us to construct a convex confidence set based on only the \textit{existence} of an online learning algorithm with a regret guarantee. Using R2CS, we obtain a strict improvement in the regret bound w.r.t. π in logistic bandits while retaining computational feasibility and the dependence on other factors such as π and π. We apply our new confidence set to the regret analyses of logistic bandits with a new martingale concentration step that circumvents an additional factor of π. We then extend this analysis to multinomial logistic bandits and obtain similar improvements in the regret, showing the efficacy of R2CS. While we applied R2CS to the (multinomial) logistic model, R2CS is a generic approach for developing confidence sets that can be used for various models, which can be of independent interest.
Papers
Paper discussed in the seminar:
- Main: Junghyun Lee, Se-Young Yun, Kwang-Sung Jun. “Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion.” In AISTATS 2024.