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Some worst-case datasets of deterministic first-order methods for solving binary logistic regression

  • * Corresponding author: Yuyuan Ouyang

    * Corresponding author: Yuyuan Ouyang 

The authors are supported by National Science Foundation grant DMS-1913006 and Office of Naval Research grant N00014-19-1-2295

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  • We present in this paper some worst-case datasets of deterministic first-order methods for solving large-scale binary logistic regression problems. Under the assumption that the number of algorithm iterations is much smaller than the problem dimension, with our worst-case datasets it requires at least $ {{{\mathcal O}}}(1/\sqrt{\varepsilon}) $ first-order oracle inquiries to compute an $ \varepsilon $-approximate solution. From traditional iteration complexity analysis point of view, the binary logistic regression loss functions with our worst-case datasets are new worst-case function instances among the class of smooth convex optimization problems.

    Mathematics Subject Classification: Primary: 90C06, 90C25, 90C30.


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