Stochastic Dynamic Programming with Factored Representations

Craig Boutilier
Department of Computer Science
University of Toronto
Toronto, ON, CANADA, M5S 3H5

Richard Dearden
Department of Computer Science
University of British Columbia
Vancouver, BC, CANADA, V6T 1Z4

Moises Goldszmidt
Computer Science Department
Stanford University
Stanford, CA 94305-9010, U.S.A.

Markov decision processes (MDPs) have proven to be popular models for decision-theoretic planning, but standard dynamic programming algorithms for solving MDPs rely on explicit, state-based specifications and computations. To alleviate the combinatorial problems associated with such methods, we propose new representational and computational techniques for MDPs that exploit certain types of problem structure. We use dynamic Bayesian networks (with decision trees representing the local families of conditional probability distributions) to represent stochastic actions in an MDP, together with a decision-tree representation of rewards. Based on this representation, we develop versions of standard dynamic programming algorithms that directly manipulate decision-tree representations of policies and value functions. This generally obviates the need for state-by-state computation, aggregating states at the leaves of these trees and requiring computations only for each aggregate state. The key to these algorithms is a decision-theoretic generalization of classic regression analysis, in which we determine the features relevant to predicting expected value. We demonstrate the method empirically on several planning problems, showing significant savings for certain types of problems. We also identify certain classes of problems for which this technique fails to perform well and suggest extensions and related ideas that may prove useful for such problems. We also briefly describe an approximation scheme based on this approach.

Artificial Intelligence 121 (2000)

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