{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/quantum-exploration-algorithms-for-multi","title":"Quantum exploration algorithms for multi-armed bandits","arxiv_id":"2007.07049","date":"2020-07-14","proceeding":null,"authors":["Daochen Wang","Xuchen You","Tongyang Li","Andrew M. Childs"],"abstract":"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 $\\tilde{O}\\bigl(\\sqrt{\\sum_{i=2}^n\\Delta^{\\smash{-2}}_i}\\bigr)$ quantum queries, where $\\Delta_{i}$ 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. 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