论文标题
Robins-Monro增强Lagrangian的随机凸优化方法
Robins-Monro Augmented Lagrangian Method for Stochastic Convex Optimization
论文作者
论文摘要
在本文中，我们提出了一种Robbins-Monro增强拉格朗日方法（RMALM）来求解一类约束的随机凸优化，可以将其视为Robbins-Monro型随机近似方法的混合体和增强的Lagrangian Lagrangian convex优化方法。在轻度条件下，我们表明所提出的算法表现出线性收敛速率。此外，我们没有验证计算上的棘手停止标准，而是表明，具有增加子问题迭代编号的RMALM具有全局复杂性$ \ MATHCAL {O}（1/\ VAREPSILON^{1+Q} $，用于$ \ VAREPSILON $ -SONOUSTION（I.E.，I.E.， $ \ mathbb {e} \ left（\ | x^k-x^*\ |^2 \ right）<\ varepsilon $），其中$ q $是任何正数。合成和实际数据的数值结果表明，所提出的算法的表现优于现有算法。
In this paper, we propose a Robbins-Monro augmented Lagrangian method (RMALM) to solve a class of constrained stochastic convex optimization, which can be regarded as a hybrid of the Robbins-Monro type stochastic approximation method and the augmented Lagrangian method of convex optimizations. Under mild conditions, we show that the proposed algorithm exhibits a linear convergence rate. Moreover, instead of verifying a computationally intractable stopping criteria, we show that the RMALM with the increasing subproblem iteration number has a global complexity $\mathcal{O}(1/\varepsilon^{1+q})$ for the $\varepsilon$-solution (i.e., $\mathbb{E}\left(\|x^k-x^*\|^2\right) < \varepsilon$), where $q$ is any positive number. Numerical results on synthetic and real data demonstrate that the proposed algorithm outperforms the existing algorithms.
