TY - GEN

T1 - Balancing asymmetry in max-sum using split constraint factor graphs

AU - Cohen, Liel

AU - Zivan, Roie

N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2018.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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. When the constraint graph representing the problem includes multiple cycles, Max-sum might not converge and explore low quality solutions. Damping is a method that increases the chances that Max-sum will converge. Damped Max-sum (DMS) was recently found to produce high quality solutions for DCOP when combined with an anytime framework. We propose a novel method for adjusting the level of asymmetry in the factor graph, in order to achieve a balance between exploitation and exploration, when using Max-sum for solving DCOPs. By converting a standard factor graph to an equivalent split constraint factor graph (SCFG), in which each function-node is split to two function-nodes, we can control the level of asymmetry for each constraint. Our empirical results demonstrate that by applying DMS to SCFGs with a minor level of asymmetry we can find high quality solutions in a small number of iterations, even without using an anytime framework. As part of our investigation of this success, we prove that for a factor-graph with a single constraint, if this constraint is split symmetrically, Max-sum applied to the resulting cycle is guaranteed to converge to the optimal solution and demonstrate that for an asymmetric split, convergence is not guaranteed.

AB - 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. When the constraint graph representing the problem includes multiple cycles, Max-sum might not converge and explore low quality solutions. Damping is a method that increases the chances that Max-sum will converge. Damped Max-sum (DMS) was recently found to produce high quality solutions for DCOP when combined with an anytime framework. We propose a novel method for adjusting the level of asymmetry in the factor graph, in order to achieve a balance between exploitation and exploration, when using Max-sum for solving DCOPs. By converting a standard factor graph to an equivalent split constraint factor graph (SCFG), in which each function-node is split to two function-nodes, we can control the level of asymmetry for each constraint. Our empirical results demonstrate that by applying DMS to SCFGs with a minor level of asymmetry we can find high quality solutions in a small number of iterations, even without using an anytime framework. As part of our investigation of this success, we prove that for a factor-graph with a single constraint, if this constraint is split symmetrically, Max-sum applied to the resulting cycle is guaranteed to converge to the optimal solution and demonstrate that for an asymmetric split, convergence is not guaranteed.

UR - http://www.scopus.com/inward/record.url?scp=85053111802&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-98334-9_43

DO - 10.1007/978-3-319-98334-9_43

M3 - Conference contribution

AN - SCOPUS:85053111802

SN - 9783319983332

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 669

EP - 687

BT - Principles and Practice of Constraint Programming - 24th International Conference, CP 2018, Proceedings

A2 - Hooker, John

PB - Springer Verlag

T2 - 24th International Conference on the Principles and Practice of Constraint Programming, CP 2018

Y2 - 27 August 2018 through 31 August 2018

ER -