Autoregressive Bandits
Fuente:
arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913237305393152 |
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| author | Bacchiocchi, Francesco Genalti, Gianmarco Maran, Davide Mussi, Marco Restelli, Marcello Gatti, Nicola Metelli, Alberto Maria |
| author_facet | Bacchiocchi, Francesco Genalti, Gianmarco Maran, Davide Mussi, Marco Restelli, Marcello Gatti, Nicola Metelli, Alberto Maria |
| contents | Autoregressive processes naturally arise in a large variety of real-world scenarios, including stock markets, sales forecasting, weather prediction, advertising, and pricing. When facing a sequential decision-making problem in such a context, the temporal dependence between consecutive observations should be properly accounted for guaranteeing convergence to the optimal policy. In this work, we propose a novel online learning setting, namely, Autoregressive Bandits (ARBs), in which the observed reward is governed by an autoregressive process of order $k$, whose parameters depend on the chosen action. We show that, under mild assumptions on the reward process, the optimal policy can be conveniently computed. Then, we devise a new optimistic regret minimization algorithm, namely, AutoRegressive Upper Confidence Bound (AR-UCB), that suffers sublinear regret of order $\widetilde{\mathcal{O}} \left( \frac{(k+1)^{3/2}\sqrt{nT}}{(1-Γ)^2}\right)$, where $T$ is the optimization horizon, $n$ is the number of actions, and $Γ< 1$ is a stability index of the process. Finally, we empirically validate our algorithm, illustrating its advantages w.r.t. bandit baselines and its robustness to misspecification of key parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06251 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Autoregressive Bandits Bacchiocchi, Francesco Genalti, Gianmarco Maran, Davide Mussi, Marco Restelli, Marcello Gatti, Nicola Metelli, Alberto Maria Machine Learning Autoregressive processes naturally arise in a large variety of real-world scenarios, including stock markets, sales forecasting, weather prediction, advertising, and pricing. When facing a sequential decision-making problem in such a context, the temporal dependence between consecutive observations should be properly accounted for guaranteeing convergence to the optimal policy. In this work, we propose a novel online learning setting, namely, Autoregressive Bandits (ARBs), in which the observed reward is governed by an autoregressive process of order $k$, whose parameters depend on the chosen action. We show that, under mild assumptions on the reward process, the optimal policy can be conveniently computed. Then, we devise a new optimistic regret minimization algorithm, namely, AutoRegressive Upper Confidence Bound (AR-UCB), that suffers sublinear regret of order $\widetilde{\mathcal{O}} \left( \frac{(k+1)^{3/2}\sqrt{nT}}{(1-Γ)^2}\right)$, where $T$ is the optimization horizon, $n$ is the number of actions, and $Γ< 1$ is a stability index of the process. Finally, we empirically validate our algorithm, illustrating its advantages w.r.t. bandit baselines and its robustness to misspecification of key parameters. |
| title | Autoregressive Bandits |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2212.06251 |