2 research outputs found
The Complexity of Reasoning with FODD and GFODD
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a
knowledge representation that is useful in mechanizing decision theoretic
planning in relational domains. GFODDs generalize function-free first order
logic and include numerical values and numerical generalizations of existential
and universal quantification. Previous work presented heuristic inference
algorithms for GFODDs and implemented these heuristics in systems for decision
theoretic planning. In this paper, we study the complexity of the computational
problems addressed by such implementations. In particular, we study the
evaluation problem, the satisfiability problem, and the equivalence problem for
GFODDs under the assumption that the size of the intended model is given with
the problem, a restriction that guarantees decidability. Our results provide a
complete characterization placing these problems within the polynomial
hierarchy. The same characterization applies to the corresponding restriction
of problems in first order logic, giving an interesting new avenue for
efficient inference when the number of objects is bounded. Our results show
that for formulas, and for corresponding GFODDs, evaluation and
satisfiability are complete, and equivalence is
complete. For formulas evaluation is complete, satisfiability
is one level higher and is complete, and equivalence is
complete.Comment: A short version of this paper appears in AAAI 2014. Version 2
includes a reorganization and some expanded proof
Solving Relational MDPs with Exogenous Events and Additive Rewards
Abstract. We formalize a simple but natural subclass of service domains for relational planning problems with object-centered, independent exogenous events and additive rewards capturing, for example, problems in inventory control. Focusing on this subclass, we present a new symbolic planning algorithm which is the first algorithm that has explicit performance guarantees for relational MDPs with exogenous events. In particular, under some technical conditions, our planning algorithm provides a monotonic lower bound on the optimal value function. To support this algorithm we present novel evaluation and reduction techniques for generalized first order decision diagrams, a knowledge representation for realvalued functions over relational world states. Our planning algorithm uses a set of focus states, which serves as a training set, to simplify and approximate the symbolic solution, and can thus be seen to perform learning for planning. A preliminary experimental evaluation demonstrates the validity of our approach.