Quantum exploration algorithms for multi-armed bandits

TitleQuantum exploration algorithms for multi-armed bandits
Publication TypeJournal Article
Year of Publication2021
AuthorsWang, D, You, X, Li, T, Childs, AM
JournalProceedings of the 35th Conference on Artificial Intelligence (AAAI 2021)
Date Published2021

 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 O~(∑ni=2Δ−2i−−−−−−−−√) quantum queries, where Δi represents the difference between the mean reward of the best arm and the ith-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).