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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.21626 |
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| _version_ | 1866917169664622592 |
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| author | Xie, Hong Gu, Haoran Huang, Yanying Tan, Tao Lian, Defu |
| author_facet | Xie, Hong Gu, Haoran Huang, Yanying Tan, Tao Lian, Defu |
| contents | This paper proposes a variant of multiple-play stochastic bandits tailored to resource allocation problems arising from LLM applications, edge intelligence, etc. The model is composed of $M$ arms and $K$ plays. Each arm has a stochastic number of capacities, and each unit of capacity is associated with a reward function. Each play is associated with a priority weight. When multiple plays compete for the arm capacity, the arm capacity is allocated in a larger priority weight first manner. Instance independent and instance dependent regret lower bounds of $Ω( α_1 σ\sqrt{KM T} )$ and $Ω(α_1 σ^2 \frac{M}Δ \ln T)$ are proved, where $α_1$ is the largest priority weight and $σ$ characterizes the reward tail. When model parameters are given, we design an algorithm named \texttt{MSB-PRS-OffOpt} to locate the optimal play allocation policy with a computational complexity of $O(MK^3)$. Utilizing \texttt{MSB-PRS-OffOpt} as a subroutine, an approximate upper confidence bound (UCB) based algorithm is designed, which has instance independent and instance dependent regret upper bounds matching the corresponding lower bound up to factors of $ \sqrt{K \ln KT }$ and $α_1 K^2$ respectively. To this end, we address nontrivial technical challenges arising from optimizing and learning under a special nonlinear combinatorial utility function induced by the prioritized resource sharing mechanism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21626 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple-play Stochastic Bandits with Prioritized Arm Capacity Sharing Xie, Hong Gu, Haoran Huang, Yanying Tan, Tao Lian, Defu Artificial Intelligence This paper proposes a variant of multiple-play stochastic bandits tailored to resource allocation problems arising from LLM applications, edge intelligence, etc. The model is composed of $M$ arms and $K$ plays. Each arm has a stochastic number of capacities, and each unit of capacity is associated with a reward function. Each play is associated with a priority weight. When multiple plays compete for the arm capacity, the arm capacity is allocated in a larger priority weight first manner. Instance independent and instance dependent regret lower bounds of $Ω( α_1 σ\sqrt{KM T} )$ and $Ω(α_1 σ^2 \frac{M}Δ \ln T)$ are proved, where $α_1$ is the largest priority weight and $σ$ characterizes the reward tail. When model parameters are given, we design an algorithm named \texttt{MSB-PRS-OffOpt} to locate the optimal play allocation policy with a computational complexity of $O(MK^3)$. Utilizing \texttt{MSB-PRS-OffOpt} as a subroutine, an approximate upper confidence bound (UCB) based algorithm is designed, which has instance independent and instance dependent regret upper bounds matching the corresponding lower bound up to factors of $ \sqrt{K \ln KT }$ and $α_1 K^2$ respectively. To this end, we address nontrivial technical challenges arising from optimizing and learning under a special nonlinear combinatorial utility function induced by the prioritized resource sharing mechanism. |
| title | Multiple-play Stochastic Bandits with Prioritized Arm Capacity Sharing |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2512.21626 |