Quantum Exploration Algorithms for Multi-Armed Bandits

Identifying the best arm of a multi-armed bandit is central problem in optimization. We study quantum computational version this with coherent oracle access to states encoding reward probabilities each as amplitudes. Specifically, we show that can find fixed confidence using $\tilde{O}\bigl(\sqrt{\sum_{i=2}^n\Delta^{\smash{-2}}_i}\bigr)$ queries, where $\Delta_{i}$ represents difference between mean and $i^\text{th}$-best arm. This algorithm, based on variable-time amplitude amplification estimation, gives quadratic speedup compared possible classical result. also prove matching lower bound (up poly-logarithmic factors).