Close the logarithmic slack in quantum multi-armed bandit regret

Close the logarithmic slack between the \(\Omega(K\log(T/K))\) minimax regret lower bound and the \(O(K\log T)\) upper bound for quantum multi-armed bandits in the quantum reward-oracle model.

Background

The paper proves an $\Omega(K\log(T/K))$ minimax regret lower bound for quantum multi-armed bandits and notes that this nearly matches the previously known $O(K\log T)$ upper bound. The remaining gap concerns the precise logarithmic dependence on the horizon and the factor inside the logarithm. Resolving it would establish the sharp regret scale for quantum multi-armed bandits in this oracle-access model.