The MVP algorithm achieves a gap-dependent variance-aware regret bound using a new conditional total variance measure, and a matching lower bound shows this variance dependence is necessary.
Finite-time analysis of the multiarmed bandit problem
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Sharp Gap-Dependent Variance-Aware Regret Bounds for Tabular MDPs
The MVP algorithm achieves a gap-dependent variance-aware regret bound using a new conditional total variance measure, and a matching lower bound shows this variance dependence is necessary.