Symbolic Dynamic Programming for Discrete and Continuous State MDPs
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.
Cite
@article{arxiv.1202.3762,
title = {Symbolic Dynamic Programming for Discrete and Continuous State MDPs},
author = {Scott Sanner and Karina Valdivia Delgado and Leliane Nunes de Barros},
journal= {arXiv preprint arXiv:1202.3762},
year = {2012}
}