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User Association and Resource Allocation in Large Language Model Based Mobile Edge Computing System over 6G Wireless Communications

Liangxin Qian, Jun Zhao

TL;DR

This work tackles efficient delivery of LLM-based services in MEC-enabled 6G networks by introducing a collaborative adapter-training workflow wherein mobile users locally train the initial adapter layers and edge servers complete the remaining layers. The core approach, the DASHF algorithm, blends Dinkelbach's fractional programming with alternating optimization, SDR, the Hungarian method, and a new FP technique to reformulate the joint optimization into a tractable QCQP and solve it efficiently. The problem is cast as maximizing the user service-cost ratio $SCR$, balancing user-perceived service quality against total delay and energy consumption while optimizing user association, offloading ratio, and resource allocation. Empirical results show DASHF achieving higher SCR and faster convergence than baselines in a 10-user, 2-server setting, illustrating the method’s practical potential for scalable, edge-assisted LLM services in 6G networks.

Abstract

In the rapidly evolving landscape of large language models (LLMs) and mobile edge computing for 6G, the need for efficient service delivery to mobile users with constrained computational resources has become paramount. Addressing this, our paper delves into a collaborative framework for model training where user data and model adapters are shared with servers to optimize performance. Within this framework, users initially update the first several layers of the adapters while freezing the other layers of them, leveraging their local datasets. Once this step is complete, these partially trained parameters are transmitted to servers. The servers, equipped with more robust computational capabilities, then update the subsequent layers. After this training, they send the enhanced parameters back to the users. This collaborative training approach ensures that mobile users with limited computational capacities can still benefit from advanced LLM services without being burdened by exhaustive computations. Central to our methodology is the DASHF algorithm, which encapsulates the Dinkelbach algorithm, alternating optimization, semidefinite relaxation (SDR), the Hungarian method, and a pioneering fractional programming technique from a recent IEEE JSAC paper [1]. The crux of DASHF is its capability to reformulate an optimization problem as Quadratically Constrained Quadratic Programming (QCQP) via meticulously crafted transformations, making it solvable by SDR and the Hungarian algorithm. Through extensive simulations, we demonstrate the effectiveness of the DASHF algorithm, offering significant insights for the advancement of collaborative LLM service deployments.

User Association and Resource Allocation in Large Language Model Based Mobile Edge Computing System over 6G Wireless Communications

TL;DR

This work tackles efficient delivery of LLM-based services in MEC-enabled 6G networks by introducing a collaborative adapter-training workflow wherein mobile users locally train the initial adapter layers and edge servers complete the remaining layers. The core approach, the DASHF algorithm, blends Dinkelbach's fractional programming with alternating optimization, SDR, the Hungarian method, and a new FP technique to reformulate the joint optimization into a tractable QCQP and solve it efficiently. The problem is cast as maximizing the user service-cost ratio , balancing user-perceived service quality against total delay and energy consumption while optimizing user association, offloading ratio, and resource allocation. Empirical results show DASHF achieving higher SCR and faster convergence than baselines in a 10-user, 2-server setting, illustrating the method’s practical potential for scalable, edge-assisted LLM services in 6G networks.

Abstract

In the rapidly evolving landscape of large language models (LLMs) and mobile edge computing for 6G, the need for efficient service delivery to mobile users with constrained computational resources has become paramount. Addressing this, our paper delves into a collaborative framework for model training where user data and model adapters are shared with servers to optimize performance. Within this framework, users initially update the first several layers of the adapters while freezing the other layers of them, leveraging their local datasets. Once this step is complete, these partially trained parameters are transmitted to servers. The servers, equipped with more robust computational capabilities, then update the subsequent layers. After this training, they send the enhanced parameters back to the users. This collaborative training approach ensures that mobile users with limited computational capacities can still benefit from advanced LLM services without being burdened by exhaustive computations. Central to our methodology is the DASHF algorithm, which encapsulates the Dinkelbach algorithm, alternating optimization, semidefinite relaxation (SDR), the Hungarian method, and a pioneering fractional programming technique from a recent IEEE JSAC paper [1]. The crux of DASHF is its capability to reformulate an optimization problem as Quadratically Constrained Quadratic Programming (QCQP) via meticulously crafted transformations, making it solvable by SDR and the Hungarian algorithm. Through extensive simulations, we demonstrate the effectiveness of the DASHF algorithm, offering significant insights for the advancement of collaborative LLM service deployments.
Paper Structure (23 sections, 2 theorems, 12 equations, 3 figures, 1 algorithm)

This paper contains 23 sections, 2 theorems, 12 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Challenges and motivations
  4. Studied problem
  5. Main contributions
  6. LLM-Empowered MEC System and Optimization Problem Formulation
  7. System scenario
  8. System model
  9. Time consumption
  10. Energy consumption
  11. User service score
  12. Optimization Problem
  13. Our proposed DASHF Algorithm to solve the optimization problem
  14. AO Part 1: Optimize , given
  15. AO Part 2: Optimize , given
  16. ...and 8 more sections

Key Result

Theorem 1

There're matrices $\mathbf{Q}$, $\mathbf{P}_0$, $\mathbf{W}_0$, $\mathbf{P^{(\text{T1})}}$, $\mathbf{P^{(\text{T2})}}$, and $\mathbf{P^{(\text{T3})}}$ that convert Problem $\mathcal{P}_1$ into QCQP Problem $\mathcal{P}_2$:

Figures (3)

  • Figure 1: Optimizing the SCR of an LLM system with $N$ users and $M$ servers through joint optimization of user association, offloading, and resource allocation.
  • Figure 2: Convergence of the proposed Algorithms
  • Figure 3: SCR comparisons under different cases

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof