论文标题
Lipschitz路径差异功能的亚级别方法的病理动力学示例
Examples of pathological dynamics of the subgradient method for Lipschitz path-differentiable functions
论文作者
论文摘要
我们表明，即使在存在有利的假设的情况下，也可以显示出消失的步骤尺寸亚级别方法（广泛用于机器学习应用程序）。我们确定，即使有惠特尼分层的目标函数满足Kurdyka-lojasiewicz不平等，有界亚级别序列的收敛可能会失败。 Moreover, when the objective function is path-differentiable we show that various properties all may fail to occur: criticality of the limit points, convergence of the sequence, convergence in values, codimension one of the accumulation set, equality of the accumulation and essential accumulation sets, connectedness of the essential accumulation set, spontaneous slowdown, oscillation compensation, and oscillation perpendicularity to the accumulation set.
We show that the vanishing stepsize subgradient method -- widely adopted for machine learning applications -- can display rather messy behavior even in the presence of favorable assumptions. We establish that convergence of bounded subgradient sequences may fail even with a Whitney stratifiable objective function satisfying the Kurdyka-Lojasiewicz inequality. Moreover, when the objective function is path-differentiable we show that various properties all may fail to occur: criticality of the limit points, convergence of the sequence, convergence in values, codimension one of the accumulation set, equality of the accumulation and essential accumulation sets, connectedness of the essential accumulation set, spontaneous slowdown, oscillation compensation, and oscillation perpendicularity to the accumulation set.
