Escaping strict saddle points of the Moreau envelope in nonsmooth optimization
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 typical algorithms applied to the proximal subproblem yield directions that approximate the gradient of the Moreau envelope in relative terms.
PDF AbstractTasks
Datasets
Add Datasets
introduced or used in this paper
Results from the Paper
Submit
results from this paper
to get state-of-the-art GitHub badges and help the
community compare results to other papers.
Methods
No methods listed for this paper. Add
relevant methods here
