AND/OR Branch-and-Bound for Graphical Models

The paper presents and evaluates the power of a new framework for optimization in graphical models, based on AND/OR search spaces. The virtue of the AND/OR representation of the search space is that its size may be far smaller than that of a traditional OR representation. We develop our work on Constraint Optimization Problems (COP) and introduce a new generation of depth-first Branch-and-Bound algorithms that explore an AND/OR search space and use static and dynamic mini-bucket heuristics to guide the search. We focus on two optimization problems, solving Weighted CSPs (WCSP) and finding the Most Probable Explanation (MPE) in belief networks. We show that the new AND/OR approach improves considerably over the classic OR space, on a variety of benchmarks including random and real-world problems. We also demonstrate the impact of different lower bounding heuristics on Branch-and-Bound exploring AND/OR spaces.