Year: 2026
Type: preprint
Abstract: We disprove a conjecture of Davis, Drusvyatskiy, and Jiang (2026) that subdifferential regularity can be removed from the generic guarantee of convergence to local minimizers for stochastic subgradient methods. We construct a globally Lipschitz, coercive, semialgebraic function in two dimensions for which the method converges to a nonminimizing Clarke critical point. For suitable power-law stepsizes, this convergence holds for open sets of initial points and linear tilts of the objective, uniformly over all perturbation sequences within a prescribed bound.
Source: arXiv (Cornell University)
Author: Li, Jiajin
Institution: University of British Columbia
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221070289