We address the problem of aggregating an ensemble of binary classifiers in a semi-supervised setting. Recently, this problem was solved optimally using a game-theoretic approach, but that analysis was specific to the 0-1 loss. In this paper, we generalize the minimax optimal algorithm of the previous work to a very general, novel class of loss functions, including but not limited to all convex surrogates, while extending its performance and efficiency guarantees. The result is a family of parameter-free ensemble aggregation algorithms which use labeled and unla- beled data; these are as efficient as linear learning and prediction for convex risk minimization, but work without any relaxations on many non-convex loss functions. The prediction algorithms take a form familiar in decision theory, applying sigmoid functions to a generalized notion of ensemble margin, but without the assumptions typically made in margin-based learning.
View on arXiv