First-order Decision-theoretic Planning in Structured Relational Environments

First-order Decision-theoretic Planning in Structured Relational Environments Scott Patrick Sanner Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2008 We consider the general framework of first-order decision-theoretic planning in structured relational environments. Most traditional solution approaches to these planning problems ground the relational specification w.r.t. a specific domain instantiation and apply a solution approach directly to the resulting ground Markov decision process (MDP). Unfortunately, the space and time complexity of these solution algorithms scale linearly with the domain size in the best case and exponentially in the worst case. An alternate approach to grounding a relational planning problem is to lift it to a first-order MDP (FOMDP) specification. This FOMDP can then be solved directly, resulting in a domain-independent solution whose space and time complexity either do not scale with domain size or can scale sublinearly in the domain size. However, such generality does not come without its own set of challenges and the first purpose of this thesis is to explore exact and approximate solution techniques for practically solving FOMDPs. The second purpose of this thesis is to extend the FOMDP specification to succinctly capture factored actions and additive rewards while extending the exact and approximate solution techniques to directly exploit this structure. In addition, we provide a proof of correctness of the first-order symbolic dynamic programming approach w.r.t. its well-studied ground MDP counterpart.