Continuous-time multi-armed bandits under random intervention times
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917312260472832 |
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| author | Noba, Kei Pérez, José Luis Yamazaki, Kazutoshi Zhang, Qingyuan |
| author_facet | Noba, Kei Pérez, José Luis Yamazaki, Kazutoshi Zhang, Qingyuan |
| contents | This paper examines multi-armed bandits in which actions are taken at random discrete times. The model consists of $J$ independent arms. When an arm is operated, it must remain active for a random duration, modeled by the inter-arrival time of a (possibly arm-dependent) renewal process. For arms evolving as a Lévy process, we provide an explicit characterization of the Gittins index, which is known to yield an optimal strategy. Furthermore, when the inter-arrival times are exponential and the arms evolve as either a spectrally negative Lévy process, a reflected spectrally negative Lévy process, or a diffusion process, the Gittins index is explicitly characterized in terms of the scale function or diffusion characteristics, respectively. Numerical experiments are performed to support the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03661 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Continuous-time multi-armed bandits under random intervention times Noba, Kei Pérez, José Luis Yamazaki, Kazutoshi Zhang, Qingyuan Optimization and Control Probability 93E20, 60G51, 90B36 This paper examines multi-armed bandits in which actions are taken at random discrete times. The model consists of $J$ independent arms. When an arm is operated, it must remain active for a random duration, modeled by the inter-arrival time of a (possibly arm-dependent) renewal process. For arms evolving as a Lévy process, we provide an explicit characterization of the Gittins index, which is known to yield an optimal strategy. Furthermore, when the inter-arrival times are exponential and the arms evolve as either a spectrally negative Lévy process, a reflected spectrally negative Lévy process, or a diffusion process, the Gittins index is explicitly characterized in terms of the scale function or diffusion characteristics, respectively. Numerical experiments are performed to support the theoretical results. |
| title | Continuous-time multi-armed bandits under random intervention times |
| topic | Optimization and Control Probability 93E20, 60G51, 90B36 |
| url | https://arxiv.org/abs/2603.03661 |