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We formalize a simple but natural subclass of service domains for relationalplanning problems with object-centered, independent exogenous events andadditive rewards capturing, for example, problems in inventory control.Focusing on this subclass, we present a new symbolic planning algorithm whichis the first algorithm that has explicit performance guarantees for relationalMDPs with exogenous events. In particular, under some technical conditions, ourplanning algorithm provides a monotonic lower bound on the optimal valuefunction. To support this algorithm we present novel evaluation and reductiontechniques for generalized first order decision diagrams, a knowledgerepresentation for real-valued functions over relational world states. Ourplanning 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 toperform learning for planning. A preliminary experimental evaluationdemonstrates the validity of our approach.

Solving Relational MDPs with Exogenous Events and Additive Rewards