UCB-V's arm-pulling counts match the solution of a deterministic equation except at a critical variance-to-gap ratio where they oscillate, and the new regret bound depends on the optimal arm's variance.
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Precise Asymptotics and Refined Regret of Variance-Aware UCB
UCB-V's arm-pulling counts match the solution of a deterministic equation except at a critical variance-to-gap ratio where they oscillate, and the new regret bound depends on the optimal arm's variance.