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• W3173037531 abstract "In many online learning or multi-armed bandit problems, the taken actions or pulled arms are ordinal and required to be monotone over time. Examples include dynamic pricing, in which the firms use markup pricing policies to please early adopters and deter strategic waiting, and clinical trials, in which the dose allocation usually follows the dose escalation principle to prevent dose limiting toxicities. We consider the continuum-armed bandit problem when the arm sequence is required to be monotone. We show that when the unknown objective function is Lipschitz continuous, the regret is $O(T)$. When in addition the objective function is unimodal or quasiconcave, the regret is $tilde O(T^{3/4})$ under the proposed algorithm, which is also shown to be the optimal rate. This deviates from the optimal rate $tilde O(T^{2/3})$ in the continuous-armed bandit literature and demonstrates the cost to the learning efficiency brought by the monotonicity requirement." @default.
• W3173037531 created "2021-06-22" @default.
• W3173037531 creator A5077201351 @default.
• W3173037531 date "2021-06-07" @default.
• W3173037531 modified "2023-09-27" @default.
• W3173037531 title "Multi-armed Bandit Requiring Monotone Arm Sequences" @default.
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• W3173037531 hasPublicationYear "2021" @default.
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