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Algorithmic Principles For Multiclass Learning Are Hard To Come By: Limits of Regularization and Proper Learning

arXiv · AI, language, vision and robotics · article · Aug 27, 2026 · UTC

Two of the most fundamental questions in statistical learning theory are the following: which prediction problems are learnable, and how should they be learned? For the former, elegant answers often take the form of combinatorial dimensions. The latter question, however, has proved considerably more elusive: all known general-purpose multiclass learners rely on intricate orientations of exponentially large one-inclusion structures, and familiar algorithmic principles such as proper learning and regularization remain poorly understood. Motivated by prior work, we ask whether learning reduces to

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