Continuous-time multi-armed bandits under random intervention times

Fuente: arXiv
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Main Authors: Noba, Kei, Pérez, José Luis, Yamazaki, Kazutoshi, Zhang, Qingyuan
Format: Preprint
Published: 2026
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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