Structured Reachability Analysis for Markov Decision Processes

Recent research in decision theoretic planning has focussed on making the solution of Markov decision processes (MDPs) more feasible. We develop a family of algorithms for structured reachability analysis of MDPs that are suitable when an initial state (or set of states) is known. Using compact, structured representations of MDPs (e.g., Bayesian networks), our methods, which vary in the tradeoff between complexity and accuracy, produce structured descriptions of (estimated) reachable states that can be used to eliminate variables or variable values from the problem description, reducing the size of the MDP and making it easier to solve. One contribution of our work is the extension of ideas from GRAPHPLAN to deal with the distributed nature of action representations typically embodied within Bayes nets and the problem of correlated action effects. We also demonstrate that our algorithm can be made more complete by using k-ary constraints instead of binary constraints. Another contribution is the illustration of how the compact representation of reachability constraints can be exploited by several existing (exact and approximate) abstraction algorithms for MDPs.