Combining explanation based generalization with the learning of macro operators (abstract only)

Explanation-based generalization (EBG) is a learning technique which attempts to learn operational concept definitions from an explanation or proof of why a particular example is a concept instance [1,2]. One way to create such a proof is through search of some proof problem space. When the application of EBG is to learn definitions of search control concepts to improve search through a domain problem space (concepts like “Operator3 useful in this situation”), it turns out that the proof and domain problem spaces can be the same. This suggests that it would be useful to combine a previously developed technique for improving search efficiency, macro learning, with EBG. In this abstract we outline the operation of a production system, called SIGNAL, which does this.Trying to improve search control performance by combining EBG with macro learning introduces two problems to deal with: from where should the concept instances for EBG come from, and which operator compositions make useful operators? SIGNAL derives answers to these questions by examining the search performance during past problem solving attempts and identifying concept instances and macros that together correct fruitless search. The processing of a problem solving attempt takes place in three phases: the identification of search control mistakes, the creation of new macro operators, and the learning of new concept definitions using EBG. We will summarize each of these.In SIGNAL, problem solving takes place as search through a problem space. States are reached from the start state by applying the operators that form the “action” side of productions. The decision to apply one operator over another is based on the classification of the state each operator will be applied to. This is similar to LEX. During a search, SIGNAL produces a progress-graph that records each generated state and the operator applications that created it. After the search has ended, the progress-graph is fed to a reflection stage where the real work begins. Here SIGNAL backs up the classification of leaf nodes in order to determine where search control mistakes occurred. A search control mistake happens when an operator is applied before another operator which led to better states. For each mistake an “adjustment” is created. Adjustments reclassify states into categories that will force highly valued states to be reached first in later searches. SIGNAL then filters the adjustments to obtain the smallest set that achieve the desired effect. Eventually EBG is used to generalize these adjustments into sufficient concept definitions, but not until after new macros are proposed.Each are in the progress-graph represents an operator application. The reflection pass of SIGNAL labels each such are with the number of search control mistakes its operator was involved in. For macro learning, SIGNAL scans the labels along paths which lead to highly rated leaf states. It searches for patterns of the form [label-1 label-2 … label-n] where label-1 & label-n ≤ any of label-2 through label-(n-1). For each such sequence, SIGNAL creates a macro production whose action side collapses all the operator applications represented by the sequence of arcs into a single operation. The set of proposed macros is then filtered to eliminate excessive overlaps. The macros that remain can be used to avoid the intermediate problem states whose visitation resulted in the search control mistakes.After creating the set of macros, SIGNAL decides on which of the adjustments created during the reflection pass it should generalize into concept definitions. Not all of them are still necessary since the new macros avoid states along some of the paths involved in search control errors. This means that the adjustments correcting these errors can be ignored if SIGNAL insures the corresponding macro will be used in the future. With this in mind, the number of necessary adjustments drops to those in the following two categories: Those produced from the reflection pass minus those correcting mistakes which could no longer occur due to one of the new macros.One new adjustment for each new macro to recognize states to which the macro is usefully applicable.For each chosen adjustment, SIGNAL applies a form of EBG to create a sufficient concept definition. Since the domain and proof problem spaces are the same, the progress-graph serves as the EBG proof. The new definition is added to those already used to pick from amongst the set of applicable operators. Additionally, SIGNAL adds the new macros in with its existing set of productions.We described a system that integrates EBG and macro learning to improve problem solving when it takes place as problem space search. Operational concept definitions learned by EBG recognize when operators are best applicable while macro operators avoid states that are hard to classify. Since the EBG proof space and domain problem spaces are the same, concept proofs are developed simultaneously with problem solving, hence any resulting improvement in search further improves the concept definitions created by EBG. We are currently in the process of evaluating SIGNAL's performance improvements in the domain of symbolic integration.