Multiple-play Stochastic Bandits with Prioritized Arm Capacity Sharing
This work addresses resource allocation challenges in applications like LLMs and edge intelligence, but it is incremental as it extends existing bandit models with a prioritized sharing mechanism.
The paper tackles the problem of resource allocation in multiple-play stochastic bandits with prioritized capacity sharing, proving instance-independent and instance-dependent regret lower bounds and designing an algorithm with matching upper bounds up to logarithmic factors.
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.