Local Regularization Does Not Characterize Multiclass PAC Learnability
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Computer Science > Machine Learning
Title:Local Regularization Does Not Characterize Multiclass PAC Learnability
Abstract:Local regularization assigns each hypothesis a test-point-dependent score and predicts with a minimum-score hypothesis consistent with the sample. Asilis et al. asked whether this principle characterizes multiclass PAC learnability. We give a negative answer. There is a countable class of Daniely--Shalev-Shwartz dimension at most two with realizable PAC sample complexity \[ O\!\left(\frac{1}{\varepsilon}\log\frac{1}{\delta}\right), \] that no local regularizer learns. Hypotheses are edges of complete graphs and instances are tournaments. At a test tournament, the scores fix an edge ranking while the training sample independently removes competitors. Cyclic triangles force enough inversions that surviving competitors produce constant population error at arbitrarily large sample sizes.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.23449 [cs.LG] |
| (or arXiv:2607.23449v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.23449
arXiv-issued DOI via DataCite (pending registration)
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