论文标题
多军匪徒的量子探索算法
Quantum exploration algorithms for multi-armed bandits
论文作者
论文摘要
识别多臂强盗的最佳臂是强盗优化的核心问题。我们研究了此问题的量子计算版本，连贯的Oracle访问已编码每个ARM作为量子幅度的奖励概率的状态。具体而言，我们证明我们可以使用$ \ tilde {o} \ bigl（\ sqrt {\ sum _ {\ sum _ {i = 2}^nδ^{\ smash {-2}} _ i} _ i} \ bigr）$量子Quartum nighters的奖励，以$δ_{i}的差异， $ i^\ text {th} $ - 最佳手臂。与最佳经典结果相比，该算法基于可变的时间振幅扩增和估计，给出了二次加速。我们还证明了匹配的量子下限（最多可达多结合因子）。
Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization. We study a quantum computational version of this problem with coherent oracle access to states encoding the reward probabilities of each arm as quantum amplitudes. Specifically, we show that we can find the best arm with fixed confidence using $\tilde{O}\bigl(\sqrt{\sum_{i=2}^nΔ^{\smash{-2}}_i}\bigr)$ quantum queries, where $Δ_{i}$ represents the difference between the mean reward of the best arm and the $i^\text{th}$-best arm. This algorithm, based on variable-time amplitude amplification and estimation, gives a quadratic speedup compared to the best possible classical result. We also prove a matching quantum lower bound (up to poly-logarithmic factors).
