We propose perturbed proximal algorithms that can provably escape strict saddles for nonsmooth weakly convex functions. The main results are based on a novel characterization of $\epsilon$-approximate local minimum for nonsmooth functions, and recent developments on perturbed gradient methods for escaping saddle points for smooth problems. Specifically, we show that under standard assumptions, the perturbed proximal point, perturbed proximal gradient and perturbed proximal linear algorithms find $\epsilon$-approximate local minimum for nonsmooth weakly convex functions in $O(\epsilon^{-2}\log(d)^4)$ iterations, where $d$ is the dimension of the problem.

翻译：我们提议了可以避免对非光滑微软锥形功能严格使用马鞍的粗略原始算法。 主要结果基于对非光滑函数近似本地最小值的新型定性,以及最近关于为平滑问题逃离马鞍点的粗略梯度方法的发展。 具体地说,我们表明,根据标准假设,在“O”(\epsilon\ ⁇ 2 ⁇ log(d)4)$的迭代中,有不光滑的软锥形函数的粗略纯度值($\epsilon$-ap)近似本地最低值($),在“O”(\epsilon\ ⁇ 2 ⁇ log(d) ⁇ 4)$(d)$(d)$(d)是问题维度的维度。