Structured Reachability Analysis for Markov Decision Processes

TL;DR

This paper introduces structured reachability algorithms for Markov decision processes using compact representations like Bayesian networks, enabling more efficient problem-solving by reducing the state space through estimated reachable states.

Contribution

It extends GRAPHPLAN ideas to Bayesian network representations, incorporates k-ary constraints for completeness, and demonstrates how reachability constraints can improve existing abstraction algorithms.

Findings

Algorithms effectively reduce MDP size by eliminating variables.

Structured reachability aids in solving MDPs more efficiently.

Extensions handle correlated action effects and distributed action representations.

Abstract

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.