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- W4318751805 abstract "In many applications of online decision making, the environment is non-stationary and it is therefore crucial to use bandit algorithms that handle changes. Most existing approaches are designed to protect against non-smooth changes, constrained only by total variation or Lipschitzness over time, where they guarantee $tilde Theta(T^{2/3})$ regret. However, in practice environments are often changing {bf smoothly}, so such algorithms may incur higher-than-necessary regret in these settings and do not leverage information on the rate of change. We study a non-stationary two-armed bandits problem where we assume that an arm's mean reward is a $beta$-Holder function over (normalized) time, meaning it is $(beta-1)$-times Lipschitz-continuously differentiable. We show the first separation between the smooth and non-smooth regimes by presenting a policy with $tilde O(T^{3/5})$ regret for $beta=2$. We complement this result by an $Omg(T^{(beta+1)/(2beta+1)})$ lower bound for any integer $betage 1$, which matches our upper bound for $beta=2$." @default.
- W4318751805 created "2023-02-02" @default.
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- W4318751805 date "2023-01-29" @default.
- W4318751805 modified "2023-09-29" @default.
- W4318751805 title "Smooth Non-Stationary Bandits" @default.
- W4318751805 doi "https://doi.org/10.48550/arxiv.2301.12366" @default.
- W4318751805 hasPublicationYear "2023" @default.
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