New ℓ∞-self-concordant analysis and Ville's-inequality martingale control yield an online confidence bound of O(√(d log t) + B√d), leading to variance-dependent MNL bandit regret with no K dependence and only asymptotic B dependence.
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Improved Online Confidence Bounds for Multinomial Logistic Bandits
New ℓ∞-self-concordant analysis and Ville's-inequality martingale control yield an online confidence bound of O(√(d log t) + B√d), leading to variance-dependent MNL bandit regret with no K dependence and only asymptotic B dependence.