Improving Problem Solving Performance by Example Guided Reformulation

Abstract

This paper introduces a method that improves the performance of a problem solver by reformulating its domain theory into one in which functionally relevant features are explicit in the syntax. This method, in contrast to previous reformulation methods, employs sets of training examples to constrain and direct the reformulation process. The use of examples offers two advantages over purely deductive approaches: First, the examples identify the exact part of the domain theory to be reformulated. Second, a proof with examples is much simpler to construct than a general proof because it is fully instantiated. The method exploits the fact that what is relevant to a goal is syntactically explicit in successful solutions to that goal. The method first takes as input a set of training examples that “exercise” an important part of the domain theory and then applies the problem solver to explain the examples in terms of a relevant goal. Next, the set of explanations is “clustered” into cases and then generalized using the induction over explanations method, forming a set of general explanations. Finally, these general explanations are reformulated into new domain theory rules. We illustrate the method in the domain of chess. We reformulate a simple declarative encoding of legal-move to produce a new domain theory that can generate the legal moves in a tenth of the time required by the original theory. We also show how the reformulated theory can more efficiently describe the important knight-fork feature.