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This work studies regression under bounded responses in terms of excess mean squared error and proves several additional structural results about universal rates in learning with squared loss about minimax and universal exponential rates.
The upper bound proof follows by combining the known fact that AdaBoost outputs a voting classifier whose voting function has zero empirical $\gamma/2$-margin loss with what is, to the best of the authors' knowledge, a new margin-based generalization bound for voting classifiers.
The aggregation with exponential weights (AEW) estimator is not fully understood in the basic setting of model selection aggregation with squared loss. In particular, whether it is minimax-rate optimal in expectation for large enough fixed temperatures and under random design has been an open problem since its introduc...
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