UBC Theses and Dissertations
Decision graphs : algorithms and applications to influence diagram evaluation and high-level path planning under uncertainty Qi, Runping
Decision making under uncertainty has been an active research topic in decision theory, operations research and Artificial Intelligence. The main objective of this thesis is to develop a uniform approach to the computational issues of decision making under uncertainty. Towards this objective, decision graphs have been proposed as an intermediate representation for decision making problems, and a number of search algorithms have been developed for evaluating decision graphs. These algorithms are readily applicable to decision problems given in the form of decision trees and in the form of finite stage Markov decision processes. In order to apply these algorithms to decision problems given in the form of influence diagrams, a stochastic dynamic programming formulation of influence diagram evaluation has been developed and a method to systematically transform a decision making problem from an influence diagram representation to a decision graph representation is presented. Through this transformation, a decision making problem represented as an influence diagram can be solved by applying the decision graph search algorithms. One of the advantages of our method for influence diagram evaluation is its ability to exploit asymmetry in decision problems, which can result in exponential savings in computation. Some problems that can be viewed as decision problems under uncertainty, but are given neither in the form of Markov decision processes, nor in the form of influence diagrams, can also be transformed into decision graphs, though this transformation is likely to be problem-specific. One problem of this kind, namely high level navigation in uncertain environments, has been studied in detail. As a result of this case study, a decision theoretic formulation and a class of off-line path planning algorithms for the problem have been developed. Since the problem of navigation in uncertain environments is of importance in its own right, an on-line path planning algorithm with polynomial time complexity for the problem has also been developed. Initial experiments show that the on-line algorithm can result in satisfactory navigation quality.
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