Changes of problem representation: Theory and experiments

Eugene Fink

Springer-Verlag, Berlin, Germany, 2003. ISBN 3-7908-1523-3.

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Preface

The purpose of our research is to enhance the efficiency of AI problem solvers by automating representation changes. We have developed a system that improves the description of input problems and selects an appropriate search algorithm for each given problem.

Motivation. Researchers have accumulated much evidence on the importance of appropriate representations for the efficiency of AI systems. The same problem may be easy or difficult, depending on the way we describe it and on the search algorithm we use. Previous work on the automatic improvement of problem descriptions has mostly been limited to the design of individual learning algorithms. The user has traditionally been responsible for the choice of algorithms appropriate for a given problem. We present a system that integrates multiple description-changing and problem-solving algorithms. The purpose of the reported work is to formalize the concept of representation and to confirm the following hypothesis:

An effective representation-changing system can be built from three parts:

a library of problem-solving algorithms;
a library of algorithms that improve problem descriptions;
a control module that selects algorithms for each given problem.

Representation-changing system. We have supported this hypothesis by building a system that improves representations in the PRODIGY problem-solving architecture. The library of problem solvers consists of several search engines available in PRODIGY. The library of description changers contains novel algorithms for selecting primary effects, generating abstractions, and discarding irrelevant elements of a problem encoding. The control module chooses and applies appropriate description changers, reuses available descriptions, and selects problem solvers.

Improving problem description. The implemented system includes seven algorithms for improving the description of a given problem. First, we formalize the notion of primary effects of operators and give two algorithms for identifying primary effects. Second, we extend the theory of abstraction search to the PRODIGY domain language and describe two techniques for abstracting preconditions and effects of operators. Third, we present auxiliary algorithms that enhance the power of abstraction by identifying relevant features of a problem and generating partial instantiations of operators.

Top-level control. We define a space of possible representations of a given problem and view the task of changing representation as a search in this space. The top-level control mechanism guides the search, using statistical analysis of previous results, control rules, and general heuristics. First, we formalize the statistical problem involved in finding an effective representation and derive a solution to this problem. Then, we describe control rules for selecting representations and present a mechanism for the synergetic use of statistical techniques, control rules, and heuristics.