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Max-sum Revisited: The Real Power of Damping

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Autonomous Agents and Multiagent Systems (AAMAS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10643))

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Abstract

Max-sum is a version of Belief propagation, used for solving DCOPs. On tree-structured problems, Max-sum converges to the optimal solution in linear time. Unfortunately when the constraint graph representing the problem includes multiple cycles (as in many standard DCOP benchmarks), Max-sum does not converge and explores low quality solutions. Recent attempts to address this limitation proposed versions of Max-sum that guarantee convergence, by changing the constraint graph structure. Damping is a method that is often used for increasing the chances that Belief propagation will converge, however, it was not mentioned in studies that proposed Max-sum for solving DCOPs.

In this paper we investigate the effect of damping on Max-sum. We prove that, while it slows down the propagation of information among agents, on tree-structured graphs, Max-sum with damping is guaranteed to converge to the optimal solution in weakly polynomial time. Our empirical results demonstrate a drastic improvement in the performance of Max-sum, when using damping. However, in contrast to the common assumption, that it performs best when converging, we demonstrate that non converging versions perform efficient exploration, and produce high quality results, when implemented within an anytime framework. On most benchmarks, the best results were achieved using a high damping factor (A preliminary version of this paper was accepted as a two page extended abstract to a coming up conference.)

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Notes

  1. 1.

    We say that a variable is involved in a constraint if it is one of the variables the constraint refers to.

  2. 2.

    For lack of space we describe the algorithm and its extensions briefly and refer the reader to more detailed descriptions in [2, 13, 22].

  3. 3.

    t-tests established that the Damped Max-Sum anytime solutions of all values of the parameter \(\lambda \) were better on average than the anytime solutions reported for standard Max-Sum, with statistical significance of p = 0.01, and better on average than DSA’s solutions for \(\lambda \) values of 0.7 and 0.9 (except for the 0.9 version on graph coloring problems), with the same significance level.

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Authors and Affiliations

  1. Industrial Engineering and Management department, Ben Gurion University, Beer-Sheva, Israel

    Liel Cohen & Roie Zivan

Authors
  1. Liel Cohen
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  2. Roie Zivan
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Correspondence to Liel Cohen .

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Editors and Affiliations

  1. University of Central Florida, Orlando, Florida, USA

    Gita Sukthankar

  2. IIIA-CSIC, Bellaterra, Spain

    Juan A. Rodriguez-Aguilar

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Cohen, L., Zivan, R. (2017). Max-sum Revisited: The Real Power of Damping. In: Sukthankar, G., Rodriguez-Aguilar, J. (eds) Autonomous Agents and Multiagent Systems. AAMAS 2017. Lecture Notes in Computer Science(), vol 10643. Springer, Cham. https://doi.org/10.1007/978-3-319-71679-4_8

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  • DOI: https://doi.org/10.1007/978-3-319-71679-4_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71678-7

  • Online ISBN: 978-3-319-71679-4

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