Clarification to exercise 1: Winnow, as described in class, is a conservative algorithm. In other words, it only changes its hypothesis when it makes a mistake. One could imagine changing the algorithm to be non-conservative. For instance, it could perform its "halving step" (cutting in half those weights w_i for which x_i = 1) on every negative example, not just those on which it makes a mistake. Or, it could perform its "doubling step" (doubling those weights w_i for which x_i = 1) on every positive example, not just those on which it makes a mistake. Your job is to show that this latter idea is "unsafe" in that it could cause the algorithm to make an unlimited number of mistakes, even if the data is consistent with some disjunction.