N-learners problem: fusion of concepts

Given N learners each capable of learning concepts (subsets) in the sense of Valiant (1985), we are interested in combining them using a single fuser. We consider two cases. In open fusion the fuser is given the sample and the hypotheses of the individual learners; we show that a fusion rule can be obtained by formulating this problem as another learning problem. We show sufficiency conditions that ensure the composite system to be better than the best of the individual. Second, in closed fusion the fuser does not have an access to either the training sample or the hypotheses of the individual learners. By using a linear threshold fusion function (of the outputs of individual learners) we show that the composite system can be made better than the best of the statistically independent learners