Speeding Up Incomplete GDL-based Algorithms for Multi-agent Optimization with Dense Local Utilities

IJCAI, pp. 31-38, 2020.

Cited by: 0|Bibtex|Views22|DOI:https://doi.org/10.24963/ijcai.2020/5
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We demonstrate that the presence of dense utility functions or utility ties would deteriorate the performance of Generic Domain Pruning

Abstract:

Incomplete GDL-based algorithms including Max-sum and its variants are important methods for multi-agent optimization. However, they face a significant scalability challenge as the computational overhead grows exponentially with respect to the arity of each utility function. Generic Domain Pruning (GDP) technique reduces the computational...More

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Introduction
  • Distributed Constraint Optimization Problems (DCOPs) [Modi et al, 2005; Fioretto et al, 2018] are a fundamental model for multi-agent optimization and coordination, in which agents cooperatively find assignments to optimize a global objective.
  • Max-sum and its variants [Farinelli et al, 2008; Rogers et al, 2011; Zivan et al, 2017; Chen et al, 2018] are popular incomplete algorithms built upon the Generalized Distributive Law (GDL) [Aji and McEliece, 2000] and have been applied to many real-world domains due to their ability of directly handling n-ary constraints.
  • The computational effort grows exponentially with respect to the arity of each utility function, which prohibits Max-sum from scaling up to large systems
Highlights
  • Distributed Constraint Optimization Problems (DCOPs) [Modi et al, 2005; Fioretto et al, 2018] are a fundamental model for multi-agent optimization and coordination, in which agents cooperatively find assignments to optimize a global objective
  • Max-sum and its variants [Farinelli et al, 2008; Rogers et al, 2011; Zivan et al, 2017; Chen et al, 2018] are popular incomplete algorithms built upon the Generalized Distributive Law (GDL) [Aji and McEliece, 2000] and have been applied to many real-world domains due to their ability of directly handling n-ary constraints
  • We empirically evaluate the performance of Generic Domain Pruning (GDP), FDSP and our proposed algorithms when accelerating Max-sum on both random DCOPs and NetRad systems
  • We demonstrate that the presence of dense utility functions or utility ties would deteriorate the performance of GDP
  • We present a discretization mechanism which offers a tradeoff between the reconstruction overhead and pruning efficiency. We theoretically show their correctness and superiorities over GDP
  • We plan to extend our work to cope with changing utility functions in a dynamic environment
Methods
  • The quality of the lower bound is the key of effective pruning, especially when local utilities are dense.
  • Alg.1 presents the sketch of GD2P.
  • When computing a response message for a variable node xi ∈ xj, it searches for the highest utility for each assignment vi ∈ Di by exhausting the sorted entries whose local utility is no less than the running lower bound lb in a sequential order.
  • The lower bound is updated whenever a higher utility is found
Results
  • The authors generate high arity and low arity factor graphs by uniformly selecting an arity for each function node from [2,5] and [5,8], respectively.
  • FDSP outperforms domain pruning variants, it is still dominated by ART-GD2P.
  • This is due to the fact that with the sorted AND/OR trees the proposed ART-GD2P can find a high-quality lower bound quickly despite of highly-structured utility functions.
  • ART-GD2P with a large t reduces the runtimes in both preprocessing phase and pruning phase, which demonstrates the necessity of the discretization mechanism
Conclusion
  • The authors demonstrate that the presence of dense utility functions or utility ties would deteriorate the performance of GDP.
  • The authors present a discretization mechanism which offers a tradeoff between the reconstruction overhead and pruning efficiency.
  • The authors theoretically show their correctness and superiorities over GDP.
  • The authors plan to extend the work to cope with changing utility functions in a dynamic environment
Summary
  • Introduction:

    Distributed Constraint Optimization Problems (DCOPs) [Modi et al, 2005; Fioretto et al, 2018] are a fundamental model for multi-agent optimization and coordination, in which agents cooperatively find assignments to optimize a global objective.
  • Max-sum and its variants [Farinelli et al, 2008; Rogers et al, 2011; Zivan et al, 2017; Chen et al, 2018] are popular incomplete algorithms built upon the Generalized Distributive Law (GDL) [Aji and McEliece, 2000] and have been applied to many real-world domains due to their ability of directly handling n-ary constraints.
  • The computational effort grows exponentially with respect to the arity of each utility function, which prohibits Max-sum from scaling up to large systems
  • Objectives:

    The authors aim to cope with dense local utilities from the perspectives of both bound quality and search space organization and develop more efficient sorting-based acceleration algorithms.
  • The authors aim to develop more efficient sorting-based acceleration algorithms for incomplete GDL-based algorithms by alleviating the negative effect of dense local utilities
  • Methods:

    The quality of the lower bound is the key of effective pruning, especially when local utilities are dense.
  • Alg.1 presents the sketch of GD2P.
  • When computing a response message for a variable node xi ∈ xj, it searches for the highest utility for each assignment vi ∈ Di by exhausting the sorted entries whose local utility is no less than the running lower bound lb in a sequential order.
  • The lower bound is updated whenever a higher utility is found
  • Results:

    The authors generate high arity and low arity factor graphs by uniformly selecting an arity for each function node from [2,5] and [5,8], respectively.
  • FDSP outperforms domain pruning variants, it is still dominated by ART-GD2P.
  • This is due to the fact that with the sorted AND/OR trees the proposed ART-GD2P can find a high-quality lower bound quickly despite of highly-structured utility functions.
  • ART-GD2P with a large t reduces the runtimes in both preprocessing phase and pruning phase, which demonstrates the necessity of the discretization mechanism
  • Conclusion:

    The authors demonstrate that the presence of dense utility functions or utility ties would deteriorate the performance of GDP.
  • The authors present a discretization mechanism which offers a tradeoff between the reconstruction overhead and pruning efficiency.
  • The authors theoretically show their correctness and superiorities over GDP.
  • The authors plan to extend the work to cope with changing utility functions in a dynamic environment
Funding
  • This research is supported by Singapore National Research Foundation projects AISG-RP2019-0013, NSOE-TSS201901, and NTU
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