Examples of Pathological Dynamics of the Subgradient Method for Lipschitz Path-Differentiable Functions
成果类型：
Article; Early Access
署名作者：
Rios-Zertuche, Rodolfo
署名单位：
Centre National de la Recherche Scientifique (CNRS)
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2021.1241
发表日期：
2022
关键词：
摘要：
We show that the vanishing step size subgradient method-widely adopted for machine learning applications-can display rather messy behavior even in the presence of favorable assumptions. We establish that convergence of bounded subgradient sequences may fail even with a Whitney stratifiable objective function satisfying the Kurdyka-Lojasiewicz inequality. Moreover, when the objective function is path-differentiable, we show that various properties all may fail to occur: criticality of the limit points, convergence of the sequence, convergence in values, codimension one of the accumulation set, equality of the accumulation and essential accumulation sets, connectedness of the essential accumulation set, spontaneous slowdown, oscillation compensation, and oscillation perpendicularity to the accumulation set.