Machine Learning - DISCo

CHAPTER 11 ANALYTICAL LEARNING 325
sis h:
(PlayTennis = Yes) t- (Humidity 5 .30)
To summarize, this example illustrates a situation where B I+ h, but where
B A D I- h. The learned hypothesis in this case entails predictions that are not
entailed by the domain theory alone. The phrase knowledge-level learning is sometimes
used to refer to this type of learning, in which the learned hypothesis entails
predictions that go beyond those entailed by the domain theory. The set of all
predictions entailed by a set of assertions Y is often called the deductive closure
of Y. The key distinction here is that in knowledge-level learning the deductive
closure of B is a proper subset of the deductive closure of B + h.
A second example of knowledge-level analytical learning is provided by considering
a type of assertions known as determinations, which have been explored
in detail by Russell (1989) and others. Determinations assert that some attribute of
the instance is fully determined by certain other attributes, without specifying the
exact nature of the dependence. For example, consider learning the target concept
"people who speak Portuguese," and imagine we are given as a domain theory the
single determination assertion "the language spoken by a person is determined by
their nationality." Taken alone, this domain theory does not enable us to classify
any instances as positive or negative. However, if we observe that "Joe, a 23-
year-old left-handed Brazilian, speaks Portuguese," then we can conclude from
this positive example and the domain theory that "all Brazilians speak Portuguese."
Both of these examples illustrate how deductive learning can produce output
hypotheses that are not entailed by the domain theory alone. In both of these cases,
the output hypothesis h satisfies B A D I- h, but does not satisfy B I- h. In both
cases, the learner deduces a justified hypothesis that does not follow from either
the domain theory alone or the training data alone.
11.4 EXPLANATION-BASED LEARNING OF SEARCH CONTROL
KNOWLEDGE
As noted above, the practical applicability of the PROLOG-EBG algorithm is restricted
by its requirement that the domain theory be correct and complete. One
important class of learning problems where this requirement is easily satisfied is
learning to speed up complex search programs. In fact, the largest scale attempts to
apply explanation-based learning have addressed the problem of learning to control
search, or what is sometimes called "speedup" learning. For example, playing
games such as chess involves searching through a vast space of possible moves
and board positions to find the best move. Many practical scheduling and optimization
problems are easily formulated as large search problems, in which the task is
to find some move toward the goal state. In such problems the definitions of the
legal search operators, together with the definition of the search objective, provide
a complete and correct domain theory for learning search control knowledge.