Nuances in Margin Conditions Determine Gains in Active Learning

Samory Kpotufe · Gan Yuan · YUNFAN ZHAO

[ Abstract ]
Mon 28 Mar 10:15 a.m. PDT — 11:45 a.m. PDT


We consider nonparametric classification with smooth regression functions, where it is well known that notions of margin in E[Y|X] determine fast or slow rates in both active and passive learning. Here we elucidate a striking distinction between the two settings. Namely, we show that some seemingly benign nuances in notions of margin - involving the uniqueness of the Bayes classifier, and which have no apparent effect on rates in passive learning - determine whether or not any active learner can outperform passive learning rates. In particular, for Audibert-Tsybakov's margin condition (allowing general situations with non-unique Bayes classifiers), no active learner can gain over passive learning in commonly studied settings where the marginal on X is near uniform. Our results thus negate the usual intuition from past literature that active rates should improve over passive rates in nonparametric settings.

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