论文标题
随机单位介绍随机单调夹杂物的差异降低
Stochastic Halpern Iteration with Variance Reduction for Stochastic Monotone Inclusions
论文作者
论文摘要
我们研究随机单调包含问题，这些问题在机器学习应用中广泛出现，包括稳健的回归和对抗性学习。我们提出了随机止动迭代的新型变体，并降低了递归方差。在cocoercive和更一般的Lipschitz-------------设置中，我们的算法通过$ \ Mathcal {o}（\ frac {1} {1} {ε^3}）$ satoctic operator评估，以实现$ \ Mathcal {o}（\ frac {1} {1} {1} {1} {1} {1} $ \ MATHCAL {O}（\ frac {1} {ε^4}）$应用于同一问题类所需的现有单调包含求解器所需的随机操作员评估。我们进一步展示了如何将随机Halpern迭代的一种建议变体与计划的重新启动方案，以解决$ {\ Mathcal {o}}}（\ frac {\ frac {\ log（log log（1/〜log（1/〜log）} {ε^2} {ε^2}）$ stochostastic操作员评估，请选择其他敏锐度。
We study stochastic monotone inclusion problems, which widely appear in machine learning applications, including robust regression and adversarial learning. We propose novel variants of stochastic Halpern iteration with recursive variance reduction. In the cocoercive -- and more generally Lipschitz-monotone -- setup, our algorithm attains $ε$ norm of the operator with $\mathcal{O}(\frac{1}{ε^3})$ stochastic operator evaluations, which significantly improves over state of the art $\mathcal{O}(\frac{1}{ε^4})$ stochastic operator evaluations required for existing monotone inclusion solvers applied to the same problem classes. We further show how to couple one of the proposed variants of stochastic Halpern iteration with a scheduled restart scheme to solve stochastic monotone inclusion problems with ${\mathcal{O}}(\frac{\log(1/ε)}{ε^2})$ stochastic operator evaluations under additional sharpness or strong monotonicity assumptions.
