Quantum exploration algorithms for multi-armed bandits
This provides a quantum advantage for bandit optimization, which is incremental as it applies existing quantum techniques to a known problem.
The paper tackles the problem of identifying the best arm in a multi-armed bandit using quantum algorithms, achieving a quadratic speedup with a query complexity of $ ilde{O}igl(\sqrt{\sum_{i=2}^n\Delta_i^{-2}}igr)$ compared to classical methods and proving a matching lower bound.
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).