Lower Bounds for the Empirical Minimization Algorithm

@article{Mendelson2008LowerBF,
  title={Lower Bounds for the Empirical Minimization Algorithm},
  author={Shahar Mendelson},
  journal={IEEE Transactions on Information Theory},
  year={2008},
  volume={54},
  pages={3797-3803}
}
In this correspondence, we present a simple argument that proves that under mild geometric assumptions on the class F and the set of target functions T, the empirical minimization algorithm cannot yield a uniform error rate that is faster than 1/radic(k) in the function learning setup. This result holds for various loss functionals and the target functions from T that cause the slow uniform error rate are clearly exhibited. 
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