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arXiv · 2603.03661

Continuous-time multi-armed bandits under random intervention times

Kei Noba·José Luis Pérez·Kazutoshi Yamazaki·Qingyuan Zhang
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Abstract

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 L\'evy 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 L\'evy process, a reflected spectrally negative L\'evy 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.

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Kei Noba, José Luis Pérez, Kazutoshi Yamazaki, Qingyuan Zhang. 2026-03-04. Continuous-time multi-armed bandits under random intervention times. https://arxiv.org/abs/2603.03661

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