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

IJCAI, pp. 31-38, 2020.

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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

Reference

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