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.

中文翻译：

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确定性一阶方法求解二进制逻辑回归的最坏情况数据集

我们在本文中介绍了用于解决大规模二进制逻辑回归问题的确定性一阶方法的最坏情况数据集。在算法迭代次数远小于问题维度的假设下，对于我们最差的数据集，它至少需要$ {{{\ mathcal O}}}（1/1 / sqrt {\ varepsilon}）$ first-命令oracle查询以计算$ \ varepsilon $近似解。从传统的迭代复杂度分析的角度来看，具有最坏情况数据集的二元logistic回归损失函数是一类光滑凸优化问题中的新的最坏情况函数实例。