Balancing Asymmetry in Max-sum Using Split Constraint Factor Graphs

• Published in: Principles and Practice of Constraint Programming pp. 669 - 687
• Main Authors: Cohen, Liel, Zivan, Roie
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 3319983334; 9783319983332
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-98334-9_43

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.