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这项研究引入了一种用于不确定数据的复杂优化问题的新算法,使用马尔科夫链而不是独立样本. 该方法,马尔科夫链随机DCA,在深度学习应用中显示出前景.

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科学领域:

  • 优化理论 优化理论
  • 机器学习 机器学习
  • 随机过程 随机过程

背景情况:

  • 非平滑的非凸的随机差异的凸 (DC) 程序往往涉及内生不确定性.
  • 标准方法假设独立且相同分布的 (i.i.d.) 样品,这些样品并不总是可用.
  • 马科维噪声在贝叶斯推理,强化学习和高维优化中普遍存在.

研究的目的:

  • 为使用马科维噪声的直流程序开发一个随机算法.
  • 分析拟议算法的收性质.
  • 将算法应用于深度学习问题,使用部分微分方程 (PDEs) 规范化.

主要方法:

  • 一个新的算法,马尔科夫链随机DCA (MCSDCA),是基于DC算法 (DCA) 设计的.
  • 收是分析在两个不对称的和非对称的意义上.
  • 两种变体,MCSDCA-odLD和MCSDCA-udLD,是使用过度缓和和低缓的朗格文动态来开发的,用于深度学习中的PDE规范化.

主要成果:

  • 建立了MCSDCA算法,用于一类非平滑的非凸的随机直流程序与马科维噪声.
  • 为拟议的方法提供了理论的趋同保证.
  • 数字实验证明了MCSDCA变体在时间序列预测和图像分类任务中的有效性.

结论:

  • 拟议的MCSDCA算法有效地处理具有马科维噪声的非平滑的非凸的静态直流程序.
  • 通过PDE规范化对深度学习的应用在经验评估中显示出有希望的结果.
  • 该研究为缺乏i.i.d.的场景提供了一个强大的优化框架. 数据. 数据. 数据.