ERM over a union of linear feature classes achieves excess risk within a factor of two of the oracle that knows the optimal feature map, asymptotically, under size conditions on the feature set.
20 G Proof of Lemma 2 We prove a slightly more general result, from which Lemma 2 can be immediately deduced
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On the Efficiency of ERM in Feature Learning
ERM over a union of linear feature classes achieves excess risk within a factor of two of the oracle that knows the optimal feature map, asymptotically, under size conditions on the feature set.