随机倾斜以在随机凸优化中寻找驻点
Random tilts to find stationary points in stochastic convex optimization
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中文总结 AI 辅助
本文研究随机凸优化中寻找驻点的问题，提出正则化经验风险最小化结合随机倾斜扰动的方法，获得$\sqrt{d/n}$的驻点残差，并通过极小极大下界证明维度依赖性的必要性。
中文摘要 AI 辅助
我们考虑寻找随机凸函数及相关变分不等式的驻点问题。对于每个问题，我们证明正则化经验风险最小化结合随机倾斜扰动，在给定n个观测值的d维问题中，可获得阶为$\sqrt{d/n}$的驻点残差。我们提出了一些补充结果，通过提供缩放为$\sqrt{\log d / n}$的极小极大下界，表明与标准随机优化和经验风险最小化不同，某些维度依赖性是必要的。
英文摘要
We consider the problem of finding stationary points of stochastic convex functions and related variational inequalities. For each, we show that regularized empirical risk minimization, coupled with a random tilting perturbation, obtains stationarity residual order $\sqrt{d/n}$ for $d$-dimensional problems given $n$ observations. We present a few complementary results that show that some dimension dependence is necessary, in distinction from standard stochastic optimization and empirical risk minimization, by providing minimax lower bounds scaling as $\sqrt{\log d / n}$.
