Multiple-play Stochastic Bandits with Prioritized Resource Sharing

Hong Xie, Yanying Huang, Haoran Gu, Defu Lian, Enhong Chen

Keywords: Multiple-play stochastic bandit, prioritized resource sharing, regret bounds

Abstract:

This paper proposes a variant of multiple-play stochastic bandits tailored to resource allocation problems arising from LLM applications,
edge intelligence applications, etc. The proposed 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 $\Omega( \alpha_1 \sigma \sqrt{KM T} )$ and $\Omega(\alpha_1 \sigma^2 \frac{MK}{\Delta} \ln T)$ are proved, where $\alpha_1$ is the largest priority weight and $\sigma$ 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 $O(M^3K^3)$. 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 $K \sqrt{ \ln KT }$ and $\alpha_1 K$ 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.

Primary Area: reinforcement learning

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 14147