First Order Decision Diagrams for Relational MDPs

Markov decision processes capture sequential decision making under uncertainty, where an agent must choose actions so as to optimize long term reward. The paper studies efficient reasoning mechanisms for Relational Markov Decision Processes (RMDP) where world states have an internal relational struc...

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Bibliographic Details
Published inarXiv.org
Main Authors Wang, Chenggang, Joshi, Saket, Khardon, Roni
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.10.2011
Subjects
Computer Science - Artificial Intelligence
Decision making
Iterative algorithms
Markov analysis
Markov processes
Optimization
Reasoning
Representations
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Summary:Markov decision processes capture sequential decision making under uncertainty, where an agent must choose actions so as to optimize long term reward. The paper studies efficient reasoning mechanisms for Relational Markov Decision Processes (RMDP) where world states have an internal relational structure that can be naturally described in terms of objects and relations among them. Two contributions are presented. First, the paper develops First Order Decision Diagrams (FODD), a new compact representation for functions over relational structures, together with a set of operators to combine FODDs, and novel reduction techniques to keep the representation small. Second, the paper shows how FODDs can be used to develop solutions for RMDPs, where reasoning is performed at the abstract level and the resulting optimal policy is independent of domain size (number of objects) or instantiation. In particular, a variant of the value iteration algorithm is developed by using special operations over FODDs, and the algorithm is shown to converge to the optimal policy.
ISSN:2331-8422
DOI:10.48550/arxiv.1111.0068