Machine Learning - DISCo

theories to automatically improve performance at several search-intensive
planning and optimization problems.
0 Second, in many other cases it is unreasonable to assume that a perfect
domain theory is available. It is difficult to write a perfectly correct and
complete theory even for our relatively simple SafeToStack problem. A more
realistic assumption is that plausible explanations based on imperfect domain
theories must be used, rather than exact proofs based on perfect knowledge.
Nevertheless, we can begin to understand the role of explanations in learning
by considering the ideal case of perfect domain theories. In Chapter 12 we
will consider learning from imperfect domain theories.
This section presents an algorithm called PROLOG-EBG (Kedar-Cabelli and
McCarty 1987) that is representative of several explanation-based learning algorithms.
PROLOG-EBG is a sequential covering algorithm (see Chapter 10). In other
words, it operates by learning a single Horn clause rule, removing the positive
training examples covered by this rule, then iterating this process on the remaining
positive examples until no further positive examples remain uncovered. When
given a complete and correct domain theory, PROLOG-EBG is guaranteed to output
a hypothesis (set of rules) that is itself correct and that covers the observed positive
training examples. For any set of training examples, the hypothesis output
by PROLOG-EBG constitutes a set of logically sufficient conditions for the target
concept, according to the domain theory. PROLOG-EBG is a refinement of the EBG
algorithm introduced by Mitchell et al. (1986) and is similar to the EGGS algorithm
described by DeJong and Mooney (1986). The PROLOG-EBG algorithm is
summarized in Table 11.2.
11.2.1 An Illustrative Trace
To illustrate, consider again the training example and domain theory shown in
Table 11.1. As summarized in Table 11.2, the PROLOG-EBG algorithm is a sequential
covering algorithm that considers the training data incrementally. For
each new positive training example that is not yet covered by a learned Horn
clause, it forms a new Horn clause by: (1) explaining the new positive training
example, (2) analyzing this explanation to determine an appropriate generalization,
and (3) refining the current hypothesis by adding a new Horn clause rule to
cover this positive example, as well as other similar instances. Below we examine
each of these three steps in turn.
11.2.1.1 EXPLAIN THE TRAINING EXAMPLE
The first step in processing each novel training example is to construct an explanation
in terms of the domain theory, showing how this positive example satisfies
the target concept. When the domain theory is correct and complete this explanation
constitutes a proof that the training example satisfies the target concept.
When dealing with imperfect prior knowledge, the notion of explanation must be
extended to allow for plausible, approximate arguments rather than perfect proofs.