Stochastic Constraint Optimization using Propagation on Ordered Binary Decision Diagrams
This work addresses a specific bottleneck in constraint programming for relational AI, offering an incremental improvement for solving SCOPs with monotonic distributions.
The paper tackles the inefficiency of solving Stochastic Constraint Optimization Problems (SCOPs) by addressing the lack of domain consistency in earlier decomposition methods using Ordered Binary Decision Diagrams (OBDDs). It proposes a new propagator for monotonic distributions that maintains domain consistency and is linear in OBDD size, potentially improving solver efficiency.
A number of problems in relational Artificial Intelligence can be viewed as Stochastic Constraint Optimization Problems (SCOPs). These are constraint optimization problems that involve objectives or constraints with a stochastic component. Building on the recently proposed language SC-ProbLog for modeling SCOPs, we propose a new method for solving these problems. Earlier methods used Probabilistic Logic Programming (PLP) techniques to create Ordered Binary Decision Diagrams (OBDDs), which were decomposed into smaller constraints in order to exploit existing constraint programming (CP) solvers. We argue that this approach has as drawback that a decomposed representation of an OBDD does not guarantee domain consistency during search, and hence limits the efficiency of the solver. For the specific case of monotonic distributions, we suggest an alternative method for using CP in SCOP, based on the development of a new propagator; we show that this propagator is linear in the size of the OBDD, and has the potential to be more efficient than the decomposition method, as it maintains domain consistency.