The Learning Situation

  Learning can be thought of as an interaction between two logically distinct entities, the learner, L, and the teacher, T. Learning situations differ in the degree to which the responsibilities of these two entities are functionally separate.

   We can think of the responsibilities of T as:

• Providing the examples or occasions for L;
• Providing feedback concerning the correctness of L's response to an example;
• Providing a sequence or ordering in which the examples are to be presented to L.

   The responsibilities of L can be thought of as:

• Providing a response or answer to each example as presented;
• Modifying its knowledge appropriately based on the feedback from T concerning the correctness of its answer;

   Various learning situations can be envisaged by simply imagining the various ways in which these responsibilities of the logically distinct entities, T and L, are distributed over functionally distinct entities T ' and L'. At one extreme we have the case where T ' carries out all of the responsibilities enumerated above for T and similarly L' carries out those assigned to L. We can refer to this learning situation as one of Instruction. At the other extreme we can imagine the case where L' carries out the responsibilities of T as well as those of L. Here we have the extreme case of Self-Instruction. The final extreme case obtains when T ' carries out all of the responsibilities of L as well as those of T. On first blush this case would seem to make little sense. After all, the teacher already possesses the knowledge to be learned. This case is, however, also of some interest. It can be thought of as the case where T ' possesses a model of some L' and may then use that model to determine how to best carry out the responsibilities of T. This model of L', call it L'' , may or may not be "complete" and "accurate". Obviously, the relation between L' and L'' will influence the degree to which L'' appropriately informs T ' concerning how best to carry out its responsibilities in order to result in L' acquiring the knowledge that is the focus of the instruction. In addition to these extreme cases, we can also imagine cases where the responsibilities intersect; e.g., L' provides examples for L in addition to those provided by T ' to L.

   Other perversely interesting cases can be obtained by assuming that L' and T ' are not cooperatively linked in the learning situation, but rather competitively linked. For example, one such perverse situation would arise if T for one reason or another fails to reliably provide accurate feedback concerning the correctness of L's response; or provides a non-optimal learning sequence, ...

What is Learned?

   How do we determine whether L has learned some concept? How do we determine the exact nature of the concept that L may have acquired as a result of training in this learning situation?

   The figure to the right provides a basis for discussing this question. It is assumed that L possesses some or all of the procedures listed in this figure. The first and simplest procedure is referred to as Identify.

   This procedure takes as its arguments L's current understanding of the concept, C, and the example, ex, that has been provided L. The procedure returns as its value either Yes or No. We can think of this as a concept recognition task.

   The next procedures listed are generative procedures. Each of these takes as its argument L's current understanding of the concept, C and returns as its value either a positive, e+, or negative, e-, example of the concept. And finally, a procedure, Communicate, is listed which takes as its argument L's current understanding of the concept, C and returns as its value a definition of C.

   We further assume that there is a procedure, Learn, which takes a set of examples, Ex, of a concept and returns as its value C'.

   The next figure on the right lists various tests that can be defined that are responsive to the question: "What is learned?" Let C' be the learner's concept and C be the teachers concept.

   According to the first test, the recognition test, the learner's concept is indistinguishable from the teacher's if whenever the learner says Yes to an example then the teacher also says Yes. And, if whenever the learner says No to an example then the teacher also says No to that example.

   This type of recognition test has been used extensively by psychologists and it is the only viable testing procedure available when the very young or non-human species are the learners. An additional complication arises when the criterion is relaxed. For example, the learner's concept and the teacher's (experimenter's) concept are said to be indistinguishable if the learner and teacher agree most of the time. Does disagreement signal a defect in the learner's learning strategy or a defect in the teacher's teaching strategy. Or, is the concept itself ill-defined or defined in such a way that a two-valued response (Yes,No) is inadequate?

   The next test for concept indistinguishability, the generation tests, would appear to be more challenging. In this case, it is assumed that both teacher and learner can generate positive and negative examples of the concept. Note it is not required that they generate the same examples, only that they identify the examples each generates in the same way. That is, T agrees that the positive examples generated by L are positive examples, and that the negative examples are negative examples. Similarly, L agrees that the positive examples generated by T are positive examples, and that the negative examples are negative examples.

   And, finally there is a test that involves some sort of communication between L and T to determine whether their respective representations of the concept are agreed to be 'equal', This would seem to be the most direct way of determining whether L has acquired the concept of T. However, it is conceivable that T could agree that L possessed the same definition of a concept but it is still conceivable that L might be unable to reliably pass the generation and recognition tests. Up to this point we have ignored the exact nature of the concept. However, it may be that for some concepts it is impossible to define generation or communication procedures that allow a concept to be taught and learned.

Issues Involved in Concept Learning

   There have been a variety of issues that have been the focus of research in induction or concept learning. These include:

• Bias
  • Representational Bias
  • Search Bias
• History
  • Dependent on Training Sequence?
• Consistency
  • Is the hypothesis necessarily consistent with the training examples?
  • Is the hypothesis necessarily consistent with all future training examples?

Bias

   Can a learning or induction be defined that as a totally unbiased process? Does a learner simply reflect the regularities in the examples and nothing more? The learner must represent both the instances of the concept as well as the rule that defines the concept. The representation utilized is a choice, either implicitly or explicitly made from a set of possible 'languages' that might be used to represent a concept. Once a representation has been chosen, then this representation focuses our attention on some aspects of the examples and diverts our attention from others. Recall the Turing Machine example that considered the language consisting of n A's followed by n B's. This concept can be represented as 'n A's followed by n B's ' or as the concept 'an AB pair together with 0 or one additional AB pair embedded within it.' Or more formally as 'ASB where S is either the empty string or the pair AB or recursively ASB.' Here the language of recursion is used to represent the concept. In this case the representations apply to exactly the same set of examples yet the regularity is represented quite differently.

   Having chosen a representation language, the learner must search the space of hypotheses that are consistent with the training examples that have been presented. If the search is an exhaustive search, then search bias can be avoided. However, often the large number of possible hypotheses precludes the use of an exhaustive search.

History

   The training sequence; that is, the order in which the examples are presented typically affects the path that the learner follows through the space of hypothesis. Consequently, some training sequences may support a more rapid and less error prone acquisition of the correct concept. If the learner's search is not exhaustive, then it is even possible that for some training sequences the learner may never acquire the correct concept.

Consistency

   Does the learner's acquisition strategy together with the training sequence guarantee that the learner's current hypothesis will be consistent with all of the examples that have been seen? And, even if this is guaranteed, at what point, if ever, can it be guaranteed that the learner's hypothesis will be consistent with all future examples of the concept?