Lower and Upper Bounds on the Generalization of Stochastic Exponentially Concave Optimization

@inproceedings{Mahdavi2015LowerAU,
  title={Lower and Upper Bounds on the Generalization of Stochastic Exponentially Concave Optimization},
  author={Mehrdad Mahdavi and Lijun Zhang and Rong Jin},
  booktitle={COLT},
  year={2015}
}
In this paper we derive high probability lower and upper bounds on the excess risk of stochastic optimization of exponentially concave loss functions. Exponentially concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, and negative logarithm loss in portfolio management. We demonstrate an O(d log T/T ) upper bound on the excess risk of stochastic online Newton step algorithm, and an O(d/T… CONTINUE READING

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