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explaining to itself the reason for this conflict and creating a rule such as the one uses domain-independent knowledge about above The net effect is that PRODIGY possible subgoal conflicts, together with domain-specific knowledge of specific operators (eg, the fact that the robot can pick up only one block at a time), to learn useful domain-specific planning rules such as the one illustrated above The use of explanation-based learning to acquire control knowledge for PRODIGY been demonstrated in a variety of problem domains including the has simple block-stacking problem above, as well as more complex scheduling and planning problems Minton (1988) reports experiments in three problem domains, in which the learned control rules improve problem-solving efficiency by a factor of two to four Furthermore, the performance of these learned rules is comparable to that of handwritten rules across these three problem domains Minton also describes a number of extensions to the basic explanation-based learning procedure that improve its effectiveness for learning control knowledge These include methods for simplifying learned rules and for removing learned rules whose benefits are smaller than their cost A second example of a general problem-solving architecture that incorporates a form of explanation-based learning is the SOARsystem (Laird et al 1986; Newel1 1990) SOARsupports a broad variety of problem-solving strategies that means-ends planning strategy Like PRODIGY, however, SOAR subsumes PRODIGY'S learns by explaining situations in which its current search strategy leads to inefficiencies When it encounters a search choice for which it does not have a definite reflects on this search impasse, answer (eg, which operator to apply next) SOAR using weak methods such as generate-and-test to determine the correct course of action The reasoning used to resolve this impasse can be interpreted as an explanation for how to resolve similar impasses in the future SOAR uses a variant of explanation-based learning called chunking to extract the general conditions under which the same explanation applies SOAR been applied in a great number has of problem domains and has also been proposed as a psychologically plausible model of human learning processes (see Newel1 1990) PRODIGY SOAR and demonstrate that explanation-based learning methods can be successfully applied to acquire search control knowledge in a variety of problem domains Nevertheless, many or most heuristic search programs still use numerical evaluation functions similar to the one described in 1, rather than rules acquired by explanation-based learning What is the reason for this In fact, there are significant practical problems with applying EBL to learning search control First, in many cases the number of control rules that must be learned is very large (eg, many thousands of rules) As the system learns more and more control rules to improve its search, it must pay a larger and larger cost at each step to match this set of rules against the current search state Note this problem is not specific to explanation-based learning; it will occur for any system that represents its learned knowledge by a growing set of rules Efficient algorithms for matching rules can alleviate this problem, but not eliminate it completely Minton (1988) discusses strategies for empirically estimating the computational cost and benefit of each rule, learning rules only when the estimated benefits outweigh the estimated costs.

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and deleting rules later found to have negative utility He describes how using this kind of utility analysis to determine what should be learned and what should be forgotten significantly enhances the effectiveness of explanation-based learning in PRODIGY example, in a series of robot block-stacking problems, PRODIGY For encountered 328 opportunities for learning a new rule, but chose to exploit only 69 of these, and eventually reduced the learned rules to a set of 19, once low-utility rules were eliminated Tambe et al (1990) and Doorenbos (1993) discuss how to identify types of rules that will be particularly costly to match, as well as methods for re-expressing such rules in more efficient forms and methods for optimizing rule-matching algorithms Doorenbos (1993) describes how these methods enabled SOAR efficiently match a set of 100,000 learned rules in one problem domain, to without a significant increase in the cost of matching rules per state A second practical problem with applying explanation-based learning to learning search control is that in many cases it is intractable even to construct the explanations for the desired target concept For example, in chess we might wish to learn a target concept such as "states for which operator A leads toward the optimal solution" Unfortunately, to prove or explain why A leads toward the optimal solution requires explaining that every alternative operator leads to a less optimal outcome This typically requires effort exponential in the search depth Chien (1993) and Tadepalli (1990) explore methods for "lazy" or "incremental" explanation, in which heuristics are used to produce partial and approximate, but tractable, explanations Rules are extracted from these imperfect explanations as though the explanations were perfect Of course these learned rules may be incorrect due to the incomplete explanations The system accommodates this by monitoring the performance of the rule on subsequent cases If the rule subsequently makes an error, then the original explanation is incrementally elaborated to cover the new case, and a more refined rule is extracted from this incrementally improved explanation Many additional research efforts have explored the use of explanation-based learning for improving the efficiency of search-based problem solvers (for example, Mitchell 1981; Silver 1983; Shavlik 1990; Mahadevan et al 1993; Gervasio and DeJong 1994; DeJong 1994) Bennett and DeJong (1996) explore explanationbased learning for robot planning problems where the system has an imperfect domain theory that describes its world and actions Dietterich and Flann (1995) explore the integration of explanation-based learning with reinforcement learning methods discussed in 13 Mitchell and Thrun (1993) describe the application of an explanation-based neural network learning method (see the EBNN algorithm discussed in 12) to reinforcement learning problems.

The main points of this chapter include: In contrast to purely inductive learning methods that seek a hypothesis to fit the training data, purely analytical learning methods seek a hypothesis