Constraint Limited Generalization: Acquiring Procedures From Examples

Generallzatlon IS an essential part of any system that can acquire knowledge from exanIples. l argue that generallzatlon must be limited by a variety of constraints tn order to be useful This paper gives three pnnclples on how generallzatron processes should be constramed. It also describes a system for acquiring procedures from examples which IS based on these pnnclples and IS used to illustrate them. 2. Acquiring Procedures from Examples. In the standard concept acqulsttlon task. a teacher provldcs the learner with a series of examples (and possibly non-examples) of a concept. The learner must generalize these examples to obtain a descnptlon of the concept from which the examples were derived. The procedure acquisition task IS s1mIIar. a teacher provides the learner wrath a senes of traces of the execution of a procedure. Each trace wtll show the operation of the procedure in one partrcular Set of circumstances. The learner must generalize the traces to obtain a __-‘This paper reports bvolk done at the Altlflclal lntelllgence Laboratory of the Massachusetts lnstrlute 01 Technology .%p[JOrt for ihe laboratory’s altlf!cEil Ili!elllgence research IS provided In part by the Advanced Research Profccts Agency of the Department of Defense under OffIce of Naval Research contract NO014-8&C-0505 “Procedure Matcher and Acquirer descrlptlon of the procedure that will apply under all circumstances-the procedure that the teacher was using to generate the traces. For example, the teacher may snow a robot how to assemble a device In several different cases: perhaps the normal case. the case when the parts are not found rn the usual position, the case when the washer sticks during assembly. and the case when the screw holes are not aligned correctly. For each case. the teacher will lead the robot through the entire assembly task. and each trace WIII consist of the sequence of actions and the feedback paiterns after each action. From this, the robot should acquire the complete assembly procedure. Several people (e g., Mltchelt [19X3], Langley [1983] arid Anderson [1983]) have approached related problems using a prodlrctlon system representation of the procedure being acquired. Here, we wash to acquire procedures with explicrt control structure. This control structuresequencing. branching, loops. and variable reference-is not present in the example traces and must be Inferred. Therefore. we cannot use the generalization methods used in in either concept or production system acquisition In a straightforward manner. Acqulsltion of procedures with exptlclt control structure has also been studied by Van Lehn [1983] (a multi-column subtractlcn procedure) and Latombe [1983] (a robot “peg-m-hole” procedure). The Induction of finite stale automata from regular strings. and the induction of functions from Input/output pairs (see Anglum and Smith [1982]) IS related to procedure acquisition, but the goals and methods in these tasks are sufficiently different that they will not be discussed here. 2.1 Domain. PMA embodtes a procedure acqulsltlon algorithm that IS intended t0 apply to a wide variety of dnrnalns. For each domain. there is a set of legal acf~ons that can be performed In the domain and the feedback patterns thdt will result from the actions. PMA IS deslyned to acquire procedures in any dornam In which the actlons are specified by an actlon type and a set of parameters, (not necessarily numertcal), and the patterns consist of a set of pattern components. each component being speclfled by a pattern type and a list of parameters All the examples glven below wtll be tal\r?n from a simple two drmenslona! robot world which meets these crlterla. The pnmnltlve actions of this robot domain Include IlOVE. ~IOVE-U~ITiL.-C(II~TACT, ROTATE, GRASP and UNGRASP. The pararneters of the HOVE and KOVE-UNTIL-CONTACT actions consist of a vector specif;,lr-,g the distance and dlrcction of the move. the parameter of the ROTATE actlon IS an angle, and the other two actions have an empty parameter list. The pafterr? that the robot world returns In response to an action has three components: the new POSITION of the robot, given In x-y coordinates; its ORIENTATION, specified by an angle: and the CONTACT, if any, between the robot and an obstacle, specified by direction of the obstacle. 2.2 Representation. The traces (or examples) gtven to FMA by the teacher are sequences uf alternating nct/or?s and pafler~s starting with a STAKT action and endlng with a STOP actlon They WIII be represcnled by a sequence of eve/Its. each event containing a pattern and the following action. Figure 1 shows two traces the teacher might provide to teach a Simple turtle procedure for clrcumnavlgatlng obstacles. 7 he turtle procedure IS “Move towards goal; if you hit something, move perpendicularly away from the obstacle 1 step, move to the side 1 step, and try again.” The first trace results from the application of the procedure when no obstacles are present. and the second, when one small obstacle is present. 6 From: AAAI-84 Proceedings. Copyright ©1984, AAAI (www.aaai.org). All rights reserved.