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

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ {{{\mathcal O}}}(1/\sqrt{\varepsilon}) $\end{document}</tex-math></inline-formula> first-order oracle inquiries to compute an <inline-formula><tex-math id="M2">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula>-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.