Rising Rested Bandits: Lower Bounds and Efficient Algorithms
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913586989760512 |
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| author | Fiandri, Marco Metelli, Alberto Maria Trov`o, Francesco |
| author_facet | Fiandri, Marco Metelli, Alberto Maria Trov`o, Francesco |
| contents | This paper is in the field of stochastic Multi-Armed Bandits (MABs), i.e. those sequential selection techniques able to learn online using only the feedback given by the chosen option (a.k.a. $arm$). We study a particular case of the rested bandits in which the arms' expected reward is monotonically non-decreasing and concave. We study the inherent sample complexity of the regret minimization problem by deriving suitable regret lower bounds. Then, we design an algorithm for the rested case $\textit{R-ed-UCB}$, providing a regret bound depending on the properties of the instance and, under certain circumstances, of $\widetilde{\mathcal{O}}(T^{\frac{2}{3}})$. We empirically compare our algorithms with state-of-the-art methods for non-stationary MABs over several synthetically generated tasks and an online model selection problem for a real-world dataset |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rising Rested Bandits: Lower Bounds and Efficient Algorithms Fiandri, Marco Metelli, Alberto Maria Trov`o, Francesco Machine Learning This paper is in the field of stochastic Multi-Armed Bandits (MABs), i.e. those sequential selection techniques able to learn online using only the feedback given by the chosen option (a.k.a. $arm$). We study a particular case of the rested bandits in which the arms' expected reward is monotonically non-decreasing and concave. We study the inherent sample complexity of the regret minimization problem by deriving suitable regret lower bounds. Then, we design an algorithm for the rested case $\textit{R-ed-UCB}$, providing a regret bound depending on the properties of the instance and, under certain circumstances, of $\widetilde{\mathcal{O}}(T^{\frac{2}{3}})$. We empirically compare our algorithms with state-of-the-art methods for non-stationary MABs over several synthetically generated tasks and an online model selection problem for a real-world dataset |
| title | Rising Rested Bandits: Lower Bounds and Efficient Algorithms |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2411.14446 |