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- W4221140649 abstract "This work addresses a version of the two-armed Bernoulli bandit problem where the sum of the means of the arms is one (the symmetric two-armed Bernoulli bandit). In a regime where the gap between these means goes to zero as the number of prediction periods approaches infinity, i.e., the difficulty of detecting the gap increases as the sample size increases, we obtain the leading order terms of the minmax optimal regret and pseudoregret for this problem by associating each of them with a solution of a linear heat equation. Our results improve upon the previously known results; specifically, we explicitly compute these leading order terms in three different scaling regimes for the gap. Additionally, we obtain new non-asymptotic bounds for any given time horizon. Although optimal player strategies are not known for more general bandit problems, there is significant interest in considering how regret accumulates under specific player strategies, even when they are not known to be optimal. We expect that the methods of this paper should be useful in settings of that type." @default.
- W4221140649 created "2022-04-03" @default.
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- W4221140649 creator A5061813475 @default.
- W4221140649 date "2022-02-11" @default.
- W4221140649 modified "2023-09-25" @default.
- W4221140649 title "A PDE-Based Analysis of the Symmetric Two-Armed Bernoulli Bandit" @default.
- W4221140649 doi "https://doi.org/10.48550/arxiv.2202.05767" @default.
- W4221140649 hasPublicationYear "2022" @default.
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