Originally Posted by yaser
Possible target function is a notion introduced in this problem in order to make a point about learning. In general, there is one target function, albeit unknown. Here we spell out "unkown" by considering all the possibilities the target function can assume. We can afford to do that here because there is only a finite number of possibilities.
Hypotheses are the products of learning that try to approximate the target function. In this problem, we prescribe different learning scenarios that result in different hypotheses, then attempt to grade these hypotheses. We grade them according to how well each of them approximates the target function. The twist is that we consider all possible target functions and grade the hypothesis according to how well it approximates each of these possible targets.
