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非凸的零次随机ADMM方法具有较低的函数查询复杂性
IEEE transactions on pattern analysis and machine intelligence
|August 14, 2024
概括
零级方法可以解决机器学习的挑战,没有梯度. 新的ZO-SPIDER-ADMM和ZOO-ADMM+算法显著降低了对处罚的非凸问题的函数查询复杂性.
科学领域:
- 优化方法优化方法.
- 机器学习 机器学习
- 没有衍生品的优化优化.
背景情况:
- 零级方法对于机器学习至关重要,当梯度不可用或昂贵时.
- 现有的方法存在高函数查询复杂性和局限性,具有复杂的惩罚和约束.
研究的目的:
- 开发更快的零顺序方法,解决现有方法的缺点.
- 用多个不平滑的惩罚来解决非凸的有限和在线问题.
主要方法:
- 拟议的零次随机交替方向乘数方法 (ZO-SPIDER-ADMM) 用于有限和问题.
- 为在线问题开发了零级在线ADMM方法 (ZOO-ADMM+).
- 证明了对两个拟议方法的函数查询复杂性的改进.
主要成果:
- ZO-SPIDER-ADMM实现了对e-静止点的函数查询复杂度为O{\displaystyle O{\displaystyle n} 1/2) ε−2,使现有方法得到了O{\displaystyle O{\displaystyle n} 1/2) 的改进.
- ZOO-ADMM+ 实现了对 ε-静止点的函数查询复杂度为 O{\displaystyle O{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text}{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text}}}}}}}\text{\text{\text{\text{\text{\text{\text{\text}}}}}}}}}}}}}}.
- 对深度神经网络的对抗性攻击的实验验证证证了算法效率.
结论:
- 拟议的ZO-SPIDER-ADMM和ZOO-ADMM+在函数查询复杂性方面提供了显著的改进,以实现零级优化.
- 这些新的算法有效地解决了复杂的非凸问题,使用非光滑的惩罚和约束.
- 这些方法证明了实际的有效性,特别是在对深度学习模型的对抗性攻击场景中.
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