Perturbed Proximal Descent to Escape Saddle Points for Non-convex and Non-smooth Objective Functions
arXiv:1901.08958v14 citations
Originality Highly original
AI Analysis
This addresses a foundational challenge in optimization for machine learning and AI, as it extends saddle point escape methods to non-smooth functions, which is incremental but important for broader applicability.
The paper tackles the problem of finding local minimizers in non-convex and non-smooth optimization by presenting the first known results for this case, requiring a new algorithm and analysis.
We consider the problem of finding local minimizers in non-convex and non-smooth optimization. Under the assumption of strict saddle points, positive results have been derived for first-order methods. We present the first known results for the non-smooth case, which requires different analysis and a different algorithm.