Stochastic Constraint Optimization using Propagation on Ordered Binary Decision Diagrams

TL;DR

This paper introduces a new propagation-based method for solving stochastic constraint optimization problems modeled with Ordered Binary Decision Diagrams, improving efficiency by maintaining domain consistency for monotonic distributions.

Contribution

It proposes a novel propagator for SCOPs that is linear in OBDD size, offering a more efficient alternative to existing decomposition methods.

Findings

The new propagator maintains domain consistency during search.

It is linear in the size of the OBDD.

Potentially more efficient than previous decomposition approaches.

Abstract

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.