Machine Learning - DISCo

What is interesting about this chess-learning task is that humans appear to
learn such target concepts from just a handful of training examples! In fact, after
considering only the single example shown in Figure 11.1, most people would
be willing to suggest a general hypothesis for the target concept, such as "board
positions in which the black king and queen are simultaneously attacked," and
would not even consider the (equally consistent) hypothesis "board positions in
which four white pawns are still in their original locations." How is it that humans
can generalize so successfully from just this one example?
The answer appears to be that people rely heavily on explaining, or analyzing,
the training example in terms of their prior knowledge about the legal moves
of chess. If asked to explain why the training example of Figure 11.1 is a positive
example of "positions in which the queen will be lost in two moves," most people
would give an explanation similar to the following: "Because white's knight is
attacking both the king and queen, black must move out of check, thereby allowing
the knight to capture the queen." The importance of such explanations is
that they provide the information needed to rationally generalize from the details
of the training example to a correct general hypothesis. Features of the training
example that are mentioned by the explanation (e.g., the position of the white
knight, black king, and black queen) are relevant to the target concept and should
be included in the general hypothesis. In contrast, features of the example that are
not mentioned by the explanation (e.g., the fact that there are six black pawns on
the board) can be assumed to be irrelevant details.
What exactly is the prior knowledge needed by a learner to construct the
explanation in this chess example? It is simply knowledge about the legal rules of
chess: knowledge of which moves are legal for the knight and other pieces, the fact
that players must alternate moves in the game, and the fact that to win the game one
player must capture his opponent's king. Note that given just this prior knowledge
it is possible in principle to calculate the optimal chess move for any board
position. However, in practice this calculation can be frustratingly complex and
despite the fact that we humans ourselves possess this complete, perfect knowledge
of chess, we remain unable to play the game optimally. As a result, much of human
learning in chess (and in other search-intensive problems such as scheduling and
planning) involves a long process of uncovering the consequences of our prior
knowledge, guided by specific training examples encountered as we play the game.
This chapter describes learning algorithms that automatically construct and
learn from such explanations. In the remainder of this section we define more
precisely the analytical learning problem. The next section presents a particular
explanation-based learning algorithm called PROLOG-EBG. Subsequent sections
then examine the general properties of this algorithm and its relationship to inductive
learning algorithms discussed in other chapters. The final section describes
the application of explanation-based learning to improving performance at large
state-space search problems. In this chapter we consider the special case in which
explanations are generated from prior knowledge that is perfectly correct, as it is
for us humans in the above chess example. In Chapter 12 we consider the more
general case of learning when prior knowledge is only approximately correct.