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First Order Markov Decision Processes
Relational Markov Decision Processes (RMDP) are a useful abstraction for complex reinforcement learning problems and stochastic planning problems since one can develop abstract solutions for them that are independent of domain size or instantiation. This thesis develops compact representations for RMDPs and exact solution methods for RMDPs using such representations. One of the core contributions of the thesis is development of the First Order Decision Diagram (FODD), a representation that captures functions over relational structures, together with a set of operators to manipulate FODDs. FODDs offer a potentially compact representation for complex functions over relational structures and can therefore serve as underlying engine for efficient algorithms with relational structures. The second core contribution is developing exact solution methods for RMDPs based on FODD representations. In particular FODDs are used to represent value functions, transition probabilities, and domain dynamics of RMDPs. Special operations are developed to implement exact value iteration and a novel variant of policy iteration and the algorithms are shown to calculate optimal solutions for RMDPs. Finally we show how the algorithms for RMDPs using FODDs can be extended to handle relational Partially Observable MDPs.
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