论文标题
非木材非covex多级组成优化的随机亚级别方法
A Stochastic Subgradient Method for Nonsmooth Nonconvex Multi-Level Composition Optimization
论文作者
论文摘要
我们提出了一种时间尺度的随机亚级别方法，用于约束多个非滑动和非凸功能的组成的优化。假定这些功能是局部的lipschitz，并且在广义上是可区分的。仅使用对功能的值和广义衍生物的随机估计。该方法不含参数。我们通过将其与差异包含物相关联并为该系统设计非不同的Lyapunov函数来证明与概率之一的收敛。对于具有Lipschitz连续导数的功能的问题，该方法在执行具有恒定步骤的$ n $迭代之后，找到了一个满足最佳度量$ 1/\ sqrt {n} $的最佳度量的点。
We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized sense. Only stochastic estimates of the values and generalized derivatives of the functions are used. The method is parameter-free. We prove convergence with probability one of the method, by associating with it a system of differential inclusions and devising a nondifferentiable Lyapunov function for this system. For problems with functions having Lipschitz continuous derivatives, the method finds a point satisfying an optimality measure with error of order $1/\sqrt{N}$, after executing $N$ iterations with constant stepsize.
