Fast rates with high probability in exp-concave statistical learning

@inproceedings{Mehta2017FastRW,
  title={Fast rates with high probability in exp-concave statistical learning},
  author={Nishant Mehta},
  booktitle={AISTATS},
  year={2017}
}
We present an algorithm for the statistical learning setting with a bounded expconcave loss in d dimensions that obtains excess risk O(d log(1/δ)/n) with probability 1−δ. The core technique is to boost the confidence of recent in-expectation O(d/n) excess risk bounds for empirical risk minimization (ERM), without sacrificing the rate, by leveraging a Bernstein condition which holds due to exp-concavity. We also show that a regret bound for any online learner in this setting translates to a high… CONTINUE READING

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