We present a new general-purpose algorithm for learning classes of $[0,1]$-valued functions in a generalization of the prediction model, and prove a general upper bound on the expected absolute error of this algorithm in terms of a scale-sensitive generalization of the Vapnik dimension proposed by Alon, Ben-David, Cesa-Bianchi and Haussler. We give lower bounds implying that our upper bounds cannot be improved by more than a constant factor in general. We apply this result, together with techniques due to Haussler and to Benedek and Itai, to obtain new upper bounds on packing numbers in terms of this scale-sensitive notion of dimension. Using a different technique, we obtain new bounds on packing numbers in terms of Kearns and Schapire's fat-shattering function. We show how to apply both packing bounds to obtain improved general bounds on the sample complexity of agnostic learning. For each $\epsilon > 0$, we establish weaker sufficient and stronger necessary conditions for a class of $[0,1]$-valued functions to be agnostically learnable to within $\epsilon$, and to be an $\epsilon$-uniform Glivenko-Cantelli class. This is a manuscript that was accepted by JCSS, together with a correction.

翻译：我们提出了一种通用新算法，用于在预测模型的推广中学习$[0,1]$值函数类，并证明了该算法期望绝对误差的一般上界，该上界基于Alon、Ben-David、Cesa-Bianchi和Haussler提出的Vapnik维数的尺度敏感推广。我们给出了下界，表明该上界在一般情况下无法改进超过常数因子。结合Haussler以及Benedek和Itai的技术，我们将这一结果应用于获得基于该尺度敏感维数概念的包络数新上界。利用另一种技术，我们得到了基于Kearns和Schapire的fat-shattering函数的包络数新上界。我们展示了如何应用这两种包络界来改进不可知学习的样本复杂度的一般上界。对于每个$\epsilon > 0$，我们为$[0,1]$值函数类建立了更弱的充分条件和更强的必要条件，使其可在$\epsilon$误差范围内被不可知学习，并成为$\epsilon$-一致Glivenko-Cantelli类。这是一份被JCSS接收的手稿，附有勘误。