We study the online learnability of hypothesis classes with respect to arbitrary, but bounded loss functions. No characterization of online learnability is known at this level of generality. We give a new scale-sensitive combinatorial dimension, named the sequential minimax dimension, and show that it gives a tight quantitative characterization of online learnability. In addition, we show that the sequential minimax dimension subsumes most existing combinatorial dimensions in online learning theory.

翻译：我们研究了假设类在任意但有界损失函数下的在线可学习性。在这一普遍性层面上，目前尚无已知的在线可学习性刻画方法。我们提出了一种新的尺度敏感的组合维度，命名为序贯极小极大维度，并证明其给出了在线可学习性的紧致定量刻画。此外，我们表明序贯极小极大维度涵盖了在线学习理论中现有的大多数组合维度。