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Heuristics with Choice Variables: Bridging the Gap between Planning and Graphical Models

Motivated by the goal of applying inference techniques used in graphical models to planning, we introduce a novel heuristic based on the idea of choice variables, implicit multivalued variables to which no plan can assign more than one value. We adapt the recursive conditioning algorithm for calculating the probability of evidence in Bayesian networks to efficiently compute the values of this heuristic by considering problem structure and reasoning by cases about different assignments to these variables. The resulting algorithm is exponential in the treewidth of the graph describing the causal relationships between the choice variables of the problem. We present some examples of the computation of the heuristic, and discuss the issues faced in applying it to existing planning benchmarks, a goal which for now remains elusive.