Escaping Strict Saddle Points of the Moreau Envelope in Nonsmooth Optimization
研究了随机扰动梯度方法在非光滑优化中如何逃逸Moreau包络的严格鞍点，证明多种算法能以可控速率实现逃逸。
Recent work has shown that stochastically perturbed gradient methods can efficiently escape strict saddle points of smooth functions. We extend this body of work to nonsmooth optimization, by analyzing an inexact analogue of a stochastically perturbed gradient method applied to the Moreau envelope. The main conclusion is that a variety of algorithms for nonsmooth optimization can escape strict saddle points of the Moreau envelope at a controlled rate. The main technical insight is that many algorithms applied to the proximal subproblem yield directions that approximate the gradient of the Moreau envelope.