Practical solution techniques for first-order MDPs

Abstract

Many traditional solution approaches to relationally specified decision-theoretic planning problems (e.g., those stated in the probabilistic planning domain description language, or PPDDL) ground the specification with respect to a specific instantiation of domain objects and apply a solution approach directly to the resulting ground Markov decision process (MDP). Unfortunately, the space and time complexity of these grounded solution approaches are polynomial in the number of domain objects and exponential in the predicate arity and the number of nested quantifiers in the relational problem specification. An alternative to grounding a relational planning problem is to tackle the problem directly at the relational level. In this article, we propose one such approach that translates an expressive subset of the PPDDL representation to a first-order MDP (FOMDP) specification and then derives a domain-independent policy without grounding at any intermediate step. However, such generality does not come without its own set of challenges—the purpose of this article is to explore practical solution techniques for solving FOMDPs. To demonstrate the applicability of our techniques, we present proof-of-concept results of our first-order approximate linear programming (FOALP) planner on problems from the probabilistic track of the ICAPS 2004 and 2006 International Planning Competitions.