Using Distribution-Free Learning Theory to Analyze Solution Path Caching Mechan isms

Much research in machine learning has been focused on the problem of symbol-level learning (SLL), or learning improve the performance of a program given examples of its behavior on typical inputs. A common approach to symbol level learning is to use some sort of mechanism for saving and later re-using the solution paths used to solve previous search problems. Examples of such mechanisms are macro-operator learning, explanation-based learning, and chunking. However, experimental evidence that these mechanisms actually improve performance is inconclusive. This paper presents a formal framework for analysis of symbol level learning programs, and then uses this framework to investigate a series of solution path caching mechanisms which provably improve performance. The analysis of these mechanisms is illuminating in many respects; in particular, in order to obtain positive results, it is necessary to use a novel representation for a set of solution paths, and also to apply certain unusual optimizations to a set of solution paths. Several of the predictions made by the model have been connrmed by recently published experiments.