Solving Stochastic Planning Problems With Large State and Action Spaces

Thomas Dean, Robert Givan, and Kee-Eung Kim

Planning methods for deterministic planning problems traditionally exploit factored representations to encode the dynamics of problems in terms of a set of parameters, e.g., the location of a robot or the status of a piece of equipment. Factored representations achieve economy of representation by taking advantage of structure in the form of dependency relationships among these parameters. In recent work, we have addressed the problem of achieving the same economy of representation and exploiting the resulting encoding of structure for stochastic planning problems represented as Markov decision processes. In this paper, we extend our earlier work on reasoning about such factored representations to handle problems with large action spaces that are also represented in factored form, where the parameters in this case might correspond to the control parameters for different effectors on a robot or the allocations for a set of resources. The techniques described in this paper employ factored representations for Markov decision processes to identify and exploit regularities in the dynamics to expedite inference. These regularities are in the form of sets of states (described for example by boolean formulas) that behave the same with respect to sets of actions where these sets are thought of as aggregate states and aggregate actions respectively. We present theoretical foundations, describe algorithms, provide examples in which our techniques provide leverage and examples in which they fail to do so, and summarize the results of experiments with a preliminary implementation.

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