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Characterizing the Multiclass Learnability of Forgiving 0-1 Loss Functions
Jacob Trauger, Tyson Trauger, Ambuj Tewari · 2025-10-10 · via stat.ML updates on arXiv.org

In this paper we will give a characterization of the learnability of forgiving 0-1 loss functions in the multiclass setting with effectively finite cardinality of the output and label space. To do this, we create a new combinatorial dimension that is based off of the Natarajan Dimension and we show that a hypothesis class is learnable in our setting if and only if this Generalized Natarajan Dimension is finite. We also show how this dimension characterizes other known learning settings such as a vast amount of instantiations of learning with set-valued feedback and a modified version of list learning.

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