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Game-theoretic Distributed Learning Approach for Heterogeneous-cost Task Allocation with Budget Constraints

Weiyi Yang, Xiaolu Liu, Lei He, Yonghao Du, Yingwu Chen

TL;DR

This work addresses heterogeneous-cost task allocation under budget constraints (HCTAB) by formulating it as a coalition-formation game (CFG) with transferable utility and proving convergence to a stable partition via an exact potential game (EPG). It introduces a log-linear learning-based solver (LLH) augmented with a cooperative exchange (CE) strategy and a heterogeneous-cost learning (HLL) component to manage budget limits and cost variability, respectively. Theoretical results (Theorem 1) link CFG dynamics to the global objective, ensuring convergence to an optimal coalitional structure, while empirical results show LLH outperforms state-of-the-art distributed and learning-based baselines in solution quality and budget utilization; ablation confirms the individual contributions of CE and HLL. Overall, the approach delivers scalable, robust distributed task allocation for large, heterogeneous multi-agent systems under budget constraints, with practical potential in domains requiring coordinated, cost-aware collaboration.

Abstract

This paper investigates heterogeneous-cost task allocation with budget constraints (HCTAB), wherein heterogeneity is manifested through the varying capabilities and costs associated with different agents for task execution. Different from the centralized optimization-based method, the HCTAB problem is solved using a fully distributed framework, and a coalition formation game is introduced to provide a theoretical guarantee for this distributed framework. To solve the coalition formation game, a convergence-guaranteed log-linear learning algorithm based on heterogeneous cost is proposed. This algorithm incorporates two improvement strategies, namely, a cooperative exchange strategy and a heterogeneous-cost log-linear learning strategy. These strategies are specifically designed to be compatible with the heterogeneous cost and budget constraints characteristic of the HCTAB problem. Through ablation experiments, we demonstrate the effectiveness of these two improvements. Finally, numerical results show that the proposed algorithm outperforms existing task allocation algorithms and learning algorithms in terms of solving the HCTAB problem.

Game-theoretic Distributed Learning Approach for Heterogeneous-cost Task Allocation with Budget Constraints

TL;DR

This work addresses heterogeneous-cost task allocation under budget constraints (HCTAB) by formulating it as a coalition-formation game (CFG) with transferable utility and proving convergence to a stable partition via an exact potential game (EPG). It introduces a log-linear learning-based solver (LLH) augmented with a cooperative exchange (CE) strategy and a heterogeneous-cost learning (HLL) component to manage budget limits and cost variability, respectively. Theoretical results (Theorem 1) link CFG dynamics to the global objective, ensuring convergence to an optimal coalitional structure, while empirical results show LLH outperforms state-of-the-art distributed and learning-based baselines in solution quality and budget utilization; ablation confirms the individual contributions of CE and HLL. Overall, the approach delivers scalable, robust distributed task allocation for large, heterogeneous multi-agent systems under budget constraints, with practical potential in domains requiring coordinated, cost-aware collaboration.

Abstract

This paper investigates heterogeneous-cost task allocation with budget constraints (HCTAB), wherein heterogeneity is manifested through the varying capabilities and costs associated with different agents for task execution. Different from the centralized optimization-based method, the HCTAB problem is solved using a fully distributed framework, and a coalition formation game is introduced to provide a theoretical guarantee for this distributed framework. To solve the coalition formation game, a convergence-guaranteed log-linear learning algorithm based on heterogeneous cost is proposed. This algorithm incorporates two improvement strategies, namely, a cooperative exchange strategy and a heterogeneous-cost log-linear learning strategy. These strategies are specifically designed to be compatible with the heterogeneous cost and budget constraints characteristic of the HCTAB problem. Through ablation experiments, we demonstrate the effectiveness of these two improvements. Finally, numerical results show that the proposed algorithm outperforms existing task allocation algorithms and learning algorithms in terms of solving the HCTAB problem.
Paper Structure (14 sections, 20 equations, 6 figures, 3 tables, 1 algorithm)

This paper contains 14 sections, 20 equations, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Problem formulation and game modeling
  4. Problem formulation
  5. Coalition formation game
  6. Coalition formation game elements
  7. Preference orders
  8. Coalition formation rules
  9. Analysis of the stable coalition partition
  10. Algorithm design
  11. Experiments
  12. Ablation experiments
  13. Algorithm comparison experiments
  14. Conclusions

Figures (6)

  • Figure 1: Example of the CE strategy.
  • Figure 2: Diagram of the operational process of distributed methods in agent systems.
  • Figure 3: LLH gain over LLH-NCE and LLH-NHL with 600 agents at different budget rates ${{\alpha }_{s}}$.
  • Figure 4: LLH gain over LLH-NCE and LLH-NHL with 600 agents at different degrees of cost heterogeneity.
  • Figure 5: Algorithm comparison results at various budget rates.
  • ...and 1 more figures