Improving planning efficient by conceptual clustering

Abstract

Automated acquisition and organization of plan knowledge has been investigated by many researchers. Vere's THOTH (1980) induces a minimal set of relational operators that cover a training set of state to state transitions. For example, having observed the many individual transitions required to build a block tower, THOTH might formulate abstract operator descriptions that correspond to the 'classic' operators of Stack, Pick-up, etc. However, THOTH does not have a strong notion of 'good' operator organization, other than to discover a minimal set of abstractions that cover the training examples. Nonetheless, THOTH's ability to autonomously discover operator 'classes' makes it an early conceptual ancestor of the clustering approach that we propose. Unlike THOTH, STRIPS (Fikes, Hart & Nilsson, 1972) begins with a set of abstract operator descriptions and conjoins them using means-ends analysis to form plans. Moreover, STRIPS generalizes the applicability of these plans (using analytic methods in contrast to THOTH's empirical approach) and stores them for reuse. However, recent work in learning to plan indicates that a STRIPS approach to saving plans in an unconstrained manner may actually have detrimental effects on planning time: the time to search for applicable past experience may eventually surpass the cost of planning from scratch (Minton, 1988). Anderson and Farley (1988) suggests a possible way to mitigate the cost of finding applicable past knowledge. Their system, PLANERUS, generates a hierarchy based on common ADD conditions of STRIPS-like operators. ADD condition indices allow PLANERUS to find operators that reduce differences in a means-ends planner. In principle a discrimination net over ADD conditions can be very efficient, but like THOTH, PLANERUS appears to lack a strong prescription of operator class quality: its indexing method appears to require an exponential number of indices in the worst case because it groups operators based on combinations of one or more shared conditions. In this regard Minton (1988) points out that even with indexing schemes, systems must also be willing to dispose of past experiences (e.g., abstractions, ADD-condition combinations) that prove to be of low utility (e.g., infrequent). THOTH, STRIPS, and PLANERUS are important precursors to our work, but we hope to extend the ideas illustrated by these systems in several directions. First, a system like PLANERUS is designed primarily to facilitate goal-driven behavior, as its exclusive reliance on ADD-condition indexing indicates. However, work in reactive or situated planning (Schoppers, 1989) suggests that the current situation should also influence the selection of applicable operators: an ideal operator is one that achieves desirable goals and requires minimal alterations to the current situation to do so. Thus, we propose that when using STRIPS-like operators, PRE conditions, as well as ADD conditions should be used to retrieve operators that make progress towards the goal and that best fit the current conditions of the environment. In addition, operator class discovery and indexing should be controlled by a strong heuristic prescription of high utility operator and plan classes. Without these prescriptions, planning with or without the benefit of previous experience remains a search-intensive, often intractable enterprise (Ginsberg, 1989).