Stochastic Rising Bandits

• URL: http://arxiv.org/abs/2212.03798v1
• Date: Wed, 7 Dec 2022 17:30:45 GMT
• Title: Stochastic Rising Bandits
• Authors: Alberto Maria Metelli, Francesco Trov\`o, Matteo Pirola, Marcello Restelli
• Abstract summary: We study a particular case of the rested and restless bandits in which the arms' expected payoff is monotonically non-decreasing. This characteristic allows designing specifically crafted algorithms that exploit the regularity of the payoffs to provide tight regret bounds. 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.
• Score: 40.32303434592863
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 and restless bandits in which the arms' expected payoff is monotonically non-decreasing. This characteristic allows designing specifically crafted algorithms that exploit the regularity of the payoffs to provide tight regret bounds. We design an algorithm for the rested case (R-ed-UCB) and one for the restless case (R-less-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. Finally, using synthetic and real-world data, we illustrate the effectiveness of the proposed approaches compared with state-of-the-art algorithms for the non-stationary bandits.

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