Rising Rested Bandits: Lower Bounds and Efficient Algorithms

Marco Fiandri; Alberto Maria Metelli; Francesco Trov`o

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arXiv · 2411.14446

Rising Rested Bandits: Lower Bounds and Efficient Algorithms

Marco Fiandri·Alberto Maria Metelli·Francesco Trov`o

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Abstract

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

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BibTeX RIS

Marco Fiandri, Alberto Maria Metelli, Francesco Trov`o. 2024-11-06. Rising Rested Bandits: Lower Bounds and Efficient Algorithms. https://arxiv.org/abs/2411.14446

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