Rising Rested MAB with Linear Drift

Omer Amichay; Yishay Mansour

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arXiv · 2501.04403

Rising Rested MAB with Linear Drift

Omer Amichay·Yishay Mansour

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Abstract

We consider non-stationary multi-arm bandit (MAB) where the expected reward of each action follows a linear function of the number of times we executed the action. Our main result is a tight regret bound of $\tilde{\Theta}(T^{4/5}K^{3/5})$, by providing both upper and lower bounds. We extend our results to derive instance dependent regret bounds, which depend on the unknown parametrization of the linear drift of the rewards.

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Omer Amichay, Yishay Mansour. 2025-01-08. Rising Rested MAB with Linear Drift. https://arxiv.org/abs/2501.04403

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