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arXiv · 1202.3762

Symbolic Dynamic Programming for Discrete and Continuous State MDPs

Scott Sanner·Karina Valdivia Delgado·Leliane Nunes de Barros
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Abstract

Many real-world decision-theoretic planning problems can be naturally modeled with discrete and continuous state Markov decision processes (DC-MDPs). While previous work has addressed automated decision-theoretic planning for DCMDPs, optimal solutions have only been defined so far for limited settings, e.g., DC-MDPs having hyper-rectangular piecewise linear value functions. In this work, we extend symbolic dynamic programming (SDP) techniques to provide optimal solutions for a vastly expanded class of DCMDPs. To address the inherent combinatorial aspects of SDP, we introduce the XADD - a continuous variable extension of the algebraic decision diagram (ADD) - that maintains compact representations of the exact value function. Empirically, we demonstrate an implementation of SDP with XADDs on various DC-MDPs, showing the first optimal automated solutions to DCMDPs with linear and nonlinear piecewise partitioned value functions and showing the advantages of constraint-based pruning for XADDs.

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Scott Sanner, Karina Valdivia Delgado, Leliane Nunes de Barros. 2012-02-14. Symbolic Dynamic Programming for Discrete and Continuous State MDPs. https://arxiv.org/abs/1202.3762

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