## A Comparison of Analytic and Experimental Goal Regression for Machine Learning

### BibTeX

@MISC{_acomparison,

author = {},

title = {A Comparison of Analytic and Experimental Goal Regression for Machine Learning},

year = {}

}

### OpenURL

### Abstract

Recent research demonstrates the use of goal regression as an analytic technique for learning search heuristics. This paper critically examines this research and identifies essential applicability conditions for the technique. The conditions that operators be invertible and that the domain be closed with respect to the inverse operators severely limit the use of analytic goal regression. In those restricted domains which satisfy the applicability conditions, analytic goal regression only discovers required preconditions for operator application. Discovering pragmatic preconditions is beyond the capability of the technique. An alternative, called experimental goal regression, is defined which approximates the results of analytic goal regression without suffering from these limitations. I.

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Citation Context ...mpares analytic and experimental goal regression. II. Review of Research Utgoff [UTG083] demonstrates the use of goal regression to adjust the bias inherent in the concept hierarchy trees used in LEX =-=[M1TC78]-=-. Partial state descriptions are regressed through a solution path to form a composite constraint on initial states in the path. Motivating this work is the observation that the state description voca... |

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Citation Context ...HEWI72, McDE72 ]. Unfortunately, analytically inverting a procedurally defined operator appears impossible in general. A similar problem occurs if the goal description is defined procedurally. LEX-II =-=[MITC83]-=- partially circumvents this problem by providing the learning element with operator inverses. Both the domain operators and their inverses are represented procedurally. As Utgoff discovered [UTG083], ... |

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(Show Context)
Citation Context ...ent construction of multiple examples of goal regression products. One approach to example generation is perturbation [KIBL83A], which relies on inherent regularity and continuity in the search space =-=[LENA83]-=-. Given a single example, perturbation automatically generates and classifies neighboring examples. The selection of the most promising neighbors can be guided with some knowledge of the transformatio... |

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(Show Context)
Citation Context ...s the constraining applicability conditions and permits goal regression in a wide class of problem domains. Section 5 compares analytic and experimental goal regression. II. Review of Research Utgoff =-=[UTG083]-=- demonstrates the use of goal regression to adjust the bias inherent in the concept hierarchy trees used in LEX [M1TC78]. Partial state descriptions are regressed through a solution path to form a com... |

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Citation Context ...ression. The practical success of experimental goal regression relies on an efficient construction of multiple examples of goal regression products. One approach to example generation is perturbation =-=[KIBL83A]-=-, which relies on inherent regularity and continuity in the search space [LENA83]. Given a single example, perturbation automatically generates and classifies neighboring examples. The selection of th... |

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(Show Context)
Citation Context ...rter and Kibler [PORT84A] use an empirical variant of goal regression to improve the rate of learning problem solving heuristics. Their method of episodic learning discovers useful operator sequences =-=[KIBL83B]-=-. The learning is incremental and heuristics which recommend operators applied near the goal state are learned first. These heuristics are regressed through the episode to learn additional heuristic r... |

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Citation Context ... The regression of the partial state description clear (C) (for some constant C) yields the disjunction (y = C) \/clear (C). External disjunction is often precluded from concept description languages =-=[MICH83]-=- but commonly occurs in analytic goal regression products. While a disjunctive clause might be split into separate clauses, thereby eliminating the disjunction, negated clauses can also be troublesome... |

1 |
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(Show Context)
Citation Context ...al regression is that the rate of episodic learning can be dramatically improved by broadcasting the refinement of one heurbtic through an episode to enable the refinement of other heuristics. Minton =-=[MINT84]-=- demonstrates the power and potential of goal regression by showing effective learning from a single training instance. With a technique called constraint based generalization, state descriptions are ... |

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(Show Context)
Citation Context ...ly, this vocabulary is a priori domain knowledge. The significance of Utgoff's use of goal regression is that the vocabulary can be dynamically enriched during the learning process. Porter and Kibler =-=[PORT84A]-=- use an empirical variant of goal regression to improve the rate of learning problem solving heuristics. Their method of episodic learning discovers useful operator sequences [KIBL83B]. The learning i... |

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Learning Problem Solving
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(Show Context)
Citation Context ...erates and classifies neighboring examples. The selection of the most promising neighbors can be guided with some knowledge of the transformation performed by the operator. Relational operator models =-=[PORT84B]-=- are one technique for approximating operator definitions. V. An Example The following example compares analytic and experimental goal regression for learning search heuristics. The task is the algebr... |

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(Show Context)
Citation Context ...ntal goal regression, is defined which approximates the results of analytic goal regression without suffering from these limitations. I. Introduction Goal regression was first used in AI by Waldinger =-=[WALD77]-=- as a technique for detecting and analyzing goal interactions during planning. Given a goal state G and an operator OP, a goal regression product is a description of a sub-goal state 5, such that OP a... |